Jan 27

Classes Begin
Monday, January 27, 2014

Jan 31

Geometry & Topology Seminar
Mohan Ramachandran (Buffalo)
On holomorphic convexity of reductive coverings of compact Kahler surfaces
4:00PM, Fri Jan 31 2014, Math 122

I will talk about the following theorem. A reductive covering of a compact Kahler surface is holomorphically convex if it does not have two ends. This is work in collaboration with Napier.

Feb 3

Algebra Seminar
Yiqiang Li (University at Buffalo)
Quantum symmetric pairs and flag varieties.
4:00PM, Mon Feb 3 2014, Math 250

I'll present a geometric construction of the newly-discovered duality between quantum symmetric pairs and Hecke algebra of type $B$.

Feb 7

Geometry & Topology Seminar
Bill Menasco (Buffalo)
Short distances in the curve complex.
4:00PM, Fri Feb 7 2014, Math 122

We will give a preliminary report on recent joint work with Dan Margalit and Joan Birman. The focus is an algorithm for determining
whether a filling pair of curves in an orientable closed surface of genus greater than 1 has distance 3, 4, 5 or bigger. We will illustrate
the algorithm with a number of newly discovered filling pairs examples of distance 4 in genus 2 and 3 surfaces. These examples were discovered
with the aid of a computer program implementing the algorithm for distance 4 or greater. This computer program was developed by
the 2013-14 URGE cohort of Paul Glenn (UB), Kayla Morrell (Buffalo State) and Matthew Morse (UB).

Feb 11

Applied Mathematics Seminar
Avner Peleg (UB Math)
Particle simulations for propagation of multiple pulse sequences in broadband optical waveguide systems
4:00PM, Tue Feb 11 2014, Math 250

We develop and analyze a particle simulation model for propagation of multiple sequences of optical pulses (solitons) in broadband optical waveguide systems. The model, which goes beyond the usual mean-field approximation, consists of a large system of hybrid stochastic nonlinear ODEs for the optical pulse parameters (amplitude, group velocity, etc.), where coupling is due to inter-pulse interaction and stochasticity is due to bit-pattern randomness. I will describe the main challenges in carrying out multiscale simulations with the model, including compensation of average effects, which requires analysis of N-dimensional Lotka-Volterra models. I will then present the results of the simulations for the quantities characterizing system performance, such as probability density functions of pulse parameters, equal-distance two-time covariance and correlation functions, and the error probability (the bit-error-rate).

Feb 17

Algebra Seminar
Yorck Sommerhauser (University at Buffalo)
Deformed Enveloping Algebras I
4:00PM, Mon Feb 17 2014, Math 250

We explain how Yetter-Drinfel'd Hopf algebras can be used to construct deformed enveloping algebras. This construction is carried out in two steps. The first is to analyze the general form of a Hopf algebra with triangular decomposition in which the left and the middle as well as the right and the middle form Radford biproducts. This construction is the topic of the first talk.

Feb 19

Junior Algebra Seminar- David Hemmer
4:00PM, Wed Feb 19 2014, Math 122

Feb 20

UB Colloquium
James Cossey (University of Akron)
Degrees of Representations of Finite Groups
4:00PM, Thu Feb 20 2014, Math 250

A representation of a finite group G is a homomorphism from G
into a set of invertible matrices of some dimension, called the degree of
the representation. Our motivating question will be: Given the set of
degrees of the irreducible representations of a group G, what can be said
about the order and structure of the group? There are a number of results
in the literature about divisibility questions related to these degrees, but
until recently there was not much known about the relation between the
"large" degrees and the structure of G. In this talk we will discuss recent
results related to the largest degree, the ratio of the largest and smallest
(nonlinear) degree, and the average degree of a finite group G.

Feb 21

Algebra Seminar (Special Day): JP Cossey- University of Akron
Alperin weights of the symmetric group
4:00PM, Fri Feb 21 2014, Math 250

Title: Alperin weights of the symmetric group

In this talk, we will examine some recent work on the Alperin weight conjecture for the symmetric group. Alperin and Fong proved by a counting argument that the Alperin weight conjecture holds for the symmetric group. However, they did not explicitly provide a bijection between the Alperin weights of the symmetric group and a class of partitions, which are the natural combinatorial objects associated to symmetric groups. We will give some basics on weights and partitions, and then discuss a natural class of partitions associated to Alperin weights.

Feb 25

Applied Mathematics Seminar
Brian Spencer (University at Buffalo)
Symmetry-breaking in shape transitions of epitaxially-strained quantum dots
4:00PM, Tue Feb 25 2014, Math 250

During heteroepitaxial growth of solid films, quantum dots ("islands") form to relieve the elastic strain. As an island grows in size, it undergoes a shape transition from a shallow "pyramid" structure to a taller "dome" structure. We examine this shape transition using a model free-boundary problem in which the surface consists of facets with discrete orientation angles. Minimization of the elastic and surface energy gives a variational problem for the island shape. We solve this variational problem numerically to construct the bifurcation diagram of possible shapes (stable, metastable, unstable) including saddle-point barrier states. We find that the island shape transition occurs via sequential nucleation of facets and involves a highly asymmetric transition state (half-dome) which can be metastable. In addition, we find that a weakly asymmetric environment (substrate misorientation of a few degrees) is sufficient to make the highly asymmetric half-dome shape the global energy minimum.

Feb 26

Analysis Seminar
Jingbo Xia (SUNY at Buffalo)
On the problem of characterizing multipliers for the Drury-Arveson space
4:00PM, Wed Feb 26 2014, Math 250

http://www.math.buffalo.edu/%7Ehfli/Xia-spring14-abstract.pdf

Mar 3

Algebra Seminar
Yorck Sommerhauser (University at Buffalo)
Deformed Enveloping Algebras II
4:00PM, Mon Mar 3 2014, Math 250

In the previous talk, we have presented a general construction for Hopf algebras with triangular decomposition. However, this construction depended on two actions and a third structure element, which had to be given. In a second step, we now look at two Yetter-Drinfel'd Hopf algebras that are dual to each other and show how the two required actions can be constructed via the coadjoint actions. We also construct the third missing structure element from the pairing. By applying this construction to a specific example, an algebra that G. Lusztig denoted by f, we show how to obtain deformed enveloping algebras of semisimple Lie algebras.

Mar 4

Applied Mathematics Seminar
Michael Langberg (UB EE)
From "big data" to "small data": a unified framework for approximating and clustering data
4:00PM, Tue Mar 4 2014, Math 250

Information is everywhere and ever-increasing, and as such the scientific community is exploring the challenges and opportunities associated with “big data”. One of the great challenges in the study of big data is the extraction of patterns from massive and high-dimensional data sets, e.g., clustering. The field of geometric clustering is an extensively studied one with a wide spectrum of "real world" applications.

A "coreset" for a given clustering optimization problem is a "compressed" representation of the data at hand, in the sense that a solution for the clustering problem with the (small) coreset as input would yield an approximate solution to the problem with the original (larger) input. Using traditional techniques, a coreset usually implies provable linear time algorithms for the corresponding clustering problem.

In this talk I will present a unified and abstract framework that yields the efficient construction of succinct coresets for several clustering problems. Representing the data by a set F of positive functions over a ground set X, our framework forges a link between the combinatorial complexity of the function family F at hand (measured in terms of classical VC dimension) and the paradigm of coresets. Our coresets are obtained via randomized sampling according to a delicately designed sampling distribution. Examples in which our framework has been successful include the k-median, the k-line median, projective clustering, linear regression, low rank approximation, and subspace approximation problems.

Mar 5

Analysis Seminar
Henry Kim (University of Toronto)
Central limit theorem for Artin L-functions.
4:00PM, Wed Mar 5 2014, Math 250

We show that the trace of Frobenius elements of Artin L-functions formed from a family of cubic fields obeys the Gaussian distribution. The essential ingredient is the result of Taniguchi and Thorne on counting cubic fields with given splitting types at finitely many primes. This is a joint work with P.J. Cho.

Mar 6

UB Colloquium
Jenny Wilson (University of Chicago)
Four perspectives on the (pure) braid groups
4:00PM, Thu Mar 6 2014, Math 250

In this talk I will describe Artin's braid groups, and their close relationships to several families of groups and spaces: we will encounter configuration spaces of manifolds, complements of hyperplane arrangements, motion groups, and mapping class groups of punctured surfaces. These objects provide generalizations of the braid and pure braid groups spanning geometry, topology, algebra, and combinatorics. I'll describe recent work that draws on representation theory and algebraic combinatorics to establish stability results for each of these families.

Mar 7

Geometry & Topology Seminar
Jenny Wilson (University of Chicago)
Stability phenomena for sequences of representations of the classical Weyl groups
4:00PM, Fri Mar 7 2014, Math 122

Over the past two years Church, Ellenberg, Farb, and Nagpal have developed machinery for studying sequences of representations of the symmetric groups, using a concept they call an FI-module. Their work, which builds on results of Hemmer and others, provides a framework for describing various stability phenomena of these sequences. I will give an overview of their theory and describe how it generalizes to sequences of representations of the Weyl groups in type B/C and D. I will outline some applications, including stability results for the cohomology of the complements of Coxeter hyperplane arrangements.

Mar 14

Geometry & Topology Seminar
Anh Tran (Ohio State)
On the AJ conjecture for pretzel knots.
4:00PM, Fri Mar 14 2014, Math 122

This talk is about the AJ conjecture that relates two different knot invariants: the A-polynomial and the colored Jones polynomial of a knot in S^3. We will introduce the conjecture and the geometric picture behind it. We will discuss our approach to the AJ conjecture using the localized skein module. We will show that the conjecture holds true for those hyperbolic knots satisfying certain conditions, and in particular for some classes of two-bridge knots and pretzel knots. This is joint work with Thang T.Q. Le.

Mar 17

Spring Recess
Monday, March 17, 2014

Mar 24

Classes Resume
Monday, March 24, 2014

Mar 24

Algebra Seminar
Stefano Morra (University of Toronto)
Ordinary Representations in the p-Modular Langlands Program
4:00PM, Mon Mar 24 2014, Math 250

The recently established p-adic local Langlands correspondence for GL2(Qp) is a powerful tool which provides a bridge between p-adic Hodge theory and the p-adic representation theory of p-adic groups. In particular, its compatibility with global methods shows that if \rhobar: G(Q)-->GL2(Fp) is continuous, irreducible and odd then the weight part in Serre's modularity conjecture provides us with a partial description of the mod p-automorphic representation p attached to \rhobar|GQp .
When considering other groups than GL2(Qp), the theory of mod-p representations becomes extremely delicate and the information provided by the generalized Serre's conjectures is not enough to recover the local component at p of appropriate eigenspaces of algebraic automorphic forms. Accordingly, it is not clear, a priori, if there exists a purely local mod p-Langlands correspondence, compatible with the classical constructions in etale cohomology.
The aim of this talk is to give a precise account of the automorphic side in the mod-p local correspondence for GL2(Qp), in particular comparing the information coming from the local/global compatibility with purely local techniques. This provides us with a full description of p in terms of extensions between irreducible GL2(Zp)-representations (Serre weights), with applications to the mod p-cohomology of modular curves over Q with arbitrary level at p.

Mar 25

Special Colloquium- William Kath (Northwestern University)
Models of Large Deviations and Rare Events for Optical Pulses
4:00PM, Tue Mar 25 2014, Math 250

In optical systems, amplified spontaneous emission noise leads to errors if noise-induced fluctuations are large. We discuss methods for modeling large deviations in such systems. In particular, we show how the problem of finding large deviations can be formulated as a constrained optimization problem that combines the pulse evolution equation and, in some cases, a detector model. The results of the combined optimization are then used to guide importance-sampled Monte-Carlo simulations to compute error probabilities.

Mar 26

Analysis Seminar
Byung-Jay Kahng (Canisius College)
Separability idempotents in C*-algebras
4:00PM, Wed Mar 26 2014, Math 250

In this talk, we will discuss the notion of a "separability idempotent", in the (non-unital) C*-algebra framework. This is analogous to the notion in the purely algebraic setting, typically considered in the case of finite-dimensional algebras with identity. This work was motivated by the appearance of such objects in attempts to develop a general C*-algebraic theory of locally compact quantum groupoids. Discussion on quantum groupoids will be kept at a minimum in this talk, but we will give some examples that are related to quantum groupoids.

[(*) This is based on a joint work with Alfons Van Daele, at KU Leuven, Belgium.]

Apr 1

Applied Mathematics Seminar
postponed, moved to 4/22 [Stephen Anco (Brock University)]
TBA
4:00PM, Tue Apr 1 2014

TBA

Apr 4

Geometry & Topology Seminar
Robert Lipshitz (Columbia)
The Jones polynomial, Khovanov homology and Khovanov homotopy
4:00PM, Fri Apr 4 2014, Math 122

We will start by recalling the definition of the Jones polynomial and a refinement of it, called Khovanov homology. We will then introduce a further refinement, called a Khovanov homotopy type, and sketch some applications of this refinement. (This last part is joint work with Sucharit Sarkar.)

Apr 8

Applied Mathematics Seminar
David Salac (UB MAE)
Three-Dimensional Modeling of Vesicle Electrohydrodynamics
4:00PM, Tue Apr 8 2014, Math 250

Membranes that surround cells are composed primarily of lipid bilayers. Giant unilamellar vesicles, which are cell-sized membrane envelopes have shown promise as model systems for more complicated biological cells and in various biotechnologies such as drug-delivery systems. The application of electric fields has been proposed as a mechanism to control the dynamics of vesicles to aid in the development of biotechnologies.

In this talk the electrohydrodynamics of a three-dimensional vesicle is investigated through the use of a combined level set/continuum surface force method. The interface is tracked using a new semi-implicit Jet level set scheme. The fluid equations take into account the inextensibility of the vesicle membrane through a tension-like parameter. The electric field is obtained by an immersed interface method for which the necessary jump conditions have been developed.

In addition to the methods results will be compared to published experimental results. The numerical results here match well with the dynamics observed experimentally.

Apr 11

Geometry & Topology Seminar
Lenhard Ng (Duke)
Knot contact homology and the augmentation polynomial
4:00PM, Fri Apr 11 2014, Math 122

Knot contact homology is a package of invariants of knots and links that
comes from counting holomorphic curves in the cotangent bundle to R^3
with boundary on the conormal bundle. Recently, one part of this
package, the augmentation polynomial, has shown up in some surprising
places, including relations to the A-polynomial, colored HOMFLY
polynomials, and physics work of Aganagic, Vafa, Gukov, and others. I
will give a brief overview of knot contact homology and discuss the
latest developments. This is partly joint work with Mina Aganagic,
Tobias Ekholm, and Cumrun Vafa.

Apr 15

Applied Mathematics Seminar
Werner Ceusters (UB Biomedical Informatics)
Principles of high quality ontology design
4:00PM, Tue Apr 15 2014, Math 250

The word ‘ontology’ was originally used to denote a now 2500 years old philosophical discipline used by scholars to find out what types of entities exist in reality and how these entities relate to each other. In the early nineties, the word was introduced in computer science to denote knowledge representations of a specific sort, roughly encompassing the vocabulary of a domain of discourse and being such that entities could be classified automatically on the basis of characteristics. Ontologies in this sense form now the basis of the semantic web. Computer science scholars have focused on building representation languages and tools to create ontologies and reason with them, but neglected the relationship between ontologies and what they are – or ought to be – about. Ontology builders now use these tools abundantly, but very often they do not understand the formal semantics behind these tools, nor the principles of good ontology design, the resuly being that the majority of ontologies available on the web are seriously flawed in many respects. The goal of this talk is to explain these principles and to demonstrate by using examples how they are typically violated.

Apr 17

Colloquium: URGE to Compute Presentations
4:00PM, Thu Apr 17 2014, Math 250

Apr 18

Geometry & Topology Seminar
Johanna Mangahas (Brown)
An algorithm to detect full irreducibility by bounding the volume of periodic free factors
4:00PM, Fri Apr 18 2014, Math 122

This is a sort of sequel (but self-contained!) to my talk last year about how to bound the length of a canonical fixed curve of a reducible mapping class, and thus get a "list-and-check" algorithm for detecting pseudo-Anosov elements, which have no fixed curves. Mapping class groups are a frequent point of reference for understanding Out(F), the group of outer automorphisms of the free group F. The "fully irreducible" elements of Out(F) are its version of pseudo-Anosov mapping classes. I'll describe an analogous list-and-check method for identifying fully irreducible elements of Out(F). This is joint with Matt Clay and Alexandra Pettet.

Apr 21

Algebra Seminar
Jiuzu Hong (Yale University)
Tensor invariants, Saturation problems and Dynkin automorphisms
4:00PM, Mon Apr 21 2014, Math 250

Let σ be a Dynkin automorphism on a connected simply-laced almost simple algebraic group G. Let G_σ be a connected almost simple algebraic group associated to G and σ, whose weights can be identified with the σ-invariant weights of G. We prove an analogue of twinning character formula in the tensor invariants setting, i.e. the dimension of the tensor invariant space of G_σ is equal to the trace of σ on the corresponding tensor invariant space of G. We also prove that the saturation property for simply- laced groups implies the saturation property for non simply-laced groups. As a consequence, we can show that the saturation factor for the spin group Spin(2n+1) is 2, which seems to be new. Our results rely on the work by Goncharov-Shen on the parametrization of basis in the tensor invariant space via the tropical points of configuration space of decorated flags. This talk is based on the joint work with Linhui Shen.

Apr 22

Applied Mathematics Seminar
Stephen Anco (Brock University)
Solitons of U(1)-invariant mKdV equations
4:00PM, Tue Apr 22 2014, Math 250

Complex, U(1)-invariant generalizations of the modified Korteweg-de Vries equation
u_t + ( a u \bar u_x + b u_x \bar u ) u + u_{xxx} =0
have applications to short wave pulses in optical fibers and deep water waves. There are two integrable cases, known as the Hirota equation (b=0) and the Sasa-Satsuma equation (b/a=3). In this talk I discuss their soliton solutions. In addition to ordinary solitary waves, these two equations are found to possess standing waves (stationary solitons), harmonically modulated solitary waves (generalized envelope solitons), and breather waves (solitons with internal oscillations). All of the solutions display interesting features and nonlinear interactions, which will be illustrated analytically and graphically.

Apr 26

Upstate NY Number Theory Conference
Saturday, April 26, 2014

Apr 28

TBA
TBA
4:00PM, Mon Apr 28 2014, Math 250

TBA

Apr 29

Applied Mathematics Seminar
Paul Bauman (UB MAE)
Computing Predictions for Complex Multiphysics Problems
4:00PM, Tue Apr 29 2014, Math 250

With the development and deployment of exascale computing resources on the horizon, computational science is beginning a revolution. Not only will larger problems be tackled, but it will be expected that the computed predictions have quantified uncertainty. To meet this demand, there will be a paradigm shift in the way scientists and engineers conduct experiments, develop algorithms and software, and utilize existing technologies towards making a prediction. In this talk, we will discuss aspects of the prediction development process for hypersonic reentry problems. The presentation will include discussion of quantifying uncertainty in experimental data and developing new infrastructure for complex, multiphysics applications. We will also highlight the impact of the prediction development process on other application areas.

May 1

Applied Mathematics Seminar
Dionyssis Mantzavinos (Notre Dame)
The “good” Boussinesq equation on the half-line.
4:00PM, Thu May 1 2014, Math 250

For initial and boundary data in appropriate Sobolev spaces, we will use the novel solution representations obtained via the "unified transform” method of Fokas in order to establish well-posedness of the so-called “good” Boussinesq equation on the half-line.

May 2

Geometry & Topology Seminar
Bill Menasco (Buffalo)
Efficient geodesics in the curve complex" or "Box, glocks and socks"
4:00PM, Fri May 2 2014, Math 122

In the curve complex it is possible to have infinitely many geodesic paths between
two vertices/curves. To deal with this non-finiteness issue, Masur and Minsky introduced the notion of tight geodesics---given any two vertices in the curve graph there are only finitely many tight geodesics between them. In this talk we will discuss a new category of geodesics that also have this finiteness property---efficient geodesics. We will then discuss possible applications. This is joint work with Joan Birman and Dan Margalit.

May 7

Analysis Seminar
Roman Holowinsky (Ohio State University)
Hybrid subconvexity for convolutions of the symmetric square
4:00PM, Wed May 7 2014, Math 250

Let f be a holomorphic cusp form of full level and weight k and g a holomorphic newform of prime level p and fixed weight. With k and p large and varying, we prove hybrid subconvexity bounds for the convolution of the symmetric square of f with g via a first moment method. This is joint work with Ritabrata Munshi and Zhi Qi.

May 8

Department Faculty Meeting
4:00PM, Thu May 8 2014, 250 Math

May 9

Last Day of Classes
Friday, May 9, 2014

May 10

Reading Days
Saturday, May 10, 2014

May 12

Semester Final Examinations
Monday, May 12, 2014

May 16

Commencement Weekend
Friday, May 16, 2014

May 27

Summer Session J Begins
Tuesday, May 27, 2014

Jul 3

Summer Session J Ends
Thursday, July 3, 2014

Jul 7

Summer Session M Begins
Monday, July 7, 2014

Aug 15

Summer Session M Ends
Friday, August 15, 2014

Aug 25

Classes Begin
Monday, August 25, 2014

Aug 29

Geometry & Topology Seminar
Organizational meeting
4:00PM, Fri Aug 29 2014, Math 122

Sep 1

Labor Day (no classes)
Monday, September 1, 2014

Sep 8

Algebra Seminar
Joseph Hundley (University at Buffalo)
Eisenstein series and unitary representations
4:00PM, Mon Sep 8 2014, Math 250

I'll report on some joint work with Stephen D. Miller of Rutgers University. We consider Eisenstein series on the exceptional adelic groups, attached to quadratic characters of the tori of these groups, and show that they have square integrable residues. From this we are able to deduce unitarity of certain representations of Lie groups as well as p-adic groups as conjectured by Arthur. I will explain how this reduces to a combinatorial problem that can be checked using a computer.

Sep 10

Analysis Seminar
Ken Davidson (University of Waterloo)
Semicrossed products by abelian semigroups
4:00PM, Wed Sep 10 2014, Math 250

If P is an abelian semigroup acting on a C*-algebra A by *-endomorphisms, then there is a universal operator algebra that encodes this action known as a semicrossed product. I will discuss two issues: whether one recover the dynamics from the semicrossed productt, and what is the C*-envelope of the semicrossed product.

Sep 12

Geometry & Topology Seminar
Margaret Doig (Syracuse)
Finite surgeries - an application of Heegaard Floer homology to a traditional knot theory question
4:00PM, Fri Sep 12 2014, Math 122

It is well known that any 3-manifold can be obtained by Dehn surgery on a link in the 3-sphere but not which ones can be obtained from a knot or which knots can produce them. We'll talk about using the Heegaard Floer ``correction terms'' or ``d-invariants'' to investigate these two questions for elliptic Seifert fibered spaces (other than lens spaces). We will see a family of examples where explicit calculations of the correction terms completely answer these questions; for a generic elliptic space, we will discuss how the invariants place a bound on the possible surgery coefficients and help identify the manifolds which may be surgery on knots.

Sep 15

Algebra Seminar
Antonio Lei (Universite Laval)
Integral Iwasawa theory of p-adic representations at non-ordinary primes.
4:00PM, Mon Sep 15 2014, Math 250

We study the Iwasawa theory of p-adic representations at non-ordinary primes, over the cyclotomic tower of a number field that is either totally real or CM. In particular, under certain technical assumptions, we construct Sprung-type Coleman maps on the local Iwasawa cohomology groups and use them to define integral p-
adic L-functions and cotorsion Selmer groups. This allows us to reformulate Perrin-Riou's main conjecture in terms of these objects, in the same fashion as Kobayashi's $\pm$-Iwasawa theory for supersingular elliptic curves.

Sep 19

Geometry & Topology Seminar
Terrence Bisson (Canisius)
Braid extended power operations
4:00PM, Fri Sep 19 2014, Math 122

Many hidden operations in algebraic topology can be described by a theory of extended powers, related to covering spaces and the homology of the symmetric groups. Early examples are Steenrod operations in mod 2 cohomology, and Dyer-Lashof operations in mod 2 homology of classifying spaces of symmetric monoidal categories.

Chas and Sullivan described operations in the rational homology of free loop spaces of manifolds; but the mod 2 homology of these spaces also have Dyer-Lashof type operations related to the homology of the braid groups. We develop a modified Q-ring theory of these operations, parallel to the Bisson-Joyal Q-ring theory for Steenrod and Dyer-Lashof operations.

Sep 22

Algebra Seminar
Dr. Chad Mangum (University at Buffalo)
Representations of Certain Twisted Toroidal Lie Algebras
4:00PM, Mon Sep 22 2014, Math 250

Representations of Lie algebras, and particularly Kac-Moody algebras, have been significant in many areas of mathematics and physics for several decades. 2-Toroidal (Lie) algebras are a generalization of affine Kac-Moody algebras which possess a realization as the central extension of a loop algebra (similar to the affine case) and can be viewed as the Lie algebra of polynomial maps from the torus into a simple, finite dimensional Lie algebra. This talk will discuss a different presentation of twisted toroidal algebras (a subclass of toroidal algebras), as well as an interesting representation of that subclass using free fields.

Sep 25

Applied Mathematics Seminar
Barbara Prinari (University of Colorado at Colorado Springs)
Mathematical models for the ward atmosphere in a medical unit
4:00PM, Thu Sep 25 2014, Math 250

This talk will present recent studies aimed at analyzing the performance and clinical outcome of an existing medical unit. Two different mathematical models have been implemented and numerically tested on the basis of a four-year-long experimental data set.

The first model is of statistical nature. It is based on the time evolution equations for the population distributions over a "microscopic" state regarded as a random variable, which in the literature on generalized kinetic models is referred to as *activity*. Evolution is driven both by the interactions among the system *actors* (in our case, patients and staff), and by various external and internal events, which are suitably modelled after the experimental data available. The dynamics of the system is assumed to be connected to (and to some extent driven by) a "macroscopic" variable known in the specialized medical literature as "ward atmosphere", which refers to the perceived social and organizational climate, as well as the comfort and ease realized in the ward. Internal and external actions are taken into account by means of direct interactions and ensemble terms, and the problem, under suitable simplifying assumptions, is reduced to a sequence of correlated initial value problems for a system of 10 coupled, nonlinear, nonlocal ordinary differential equations for the probability density distributions.

The second model relies on the implementation of artificial neural networks (ANNs) to ultimately predict the ward atmosphere in the said medical unit. Specifically, we have implemented a dynamic feed-forward ANN where all the experimental data collected on a daily basis in the medical unit have been regarded as inputs/outputs of the network. An optimization of the network architecture has been carried out to identify the number of neurons, nodes in the hidden layers, network options, etc, in order to achieve the best balance between a satisfactory agreement during the training phase and the simplicity of the implementation. Advantages of the ANN technique over more traditional mathematical/statistical models are twofold: On one hand, this approach deals quite naturally with a large number of parameters/variables, and also allows to identify those variables which do not play a crucial role in the system dynamics. On the other hand, the implemented ANN can be more easily used by a staff of non-mathematicians in the unit, as an on-site predictive tool.

The predictions from the ANN technique are then compared and contrasted with those obtained from the generalized kinetic approach.


This talk is based on joint work with Enzo Serio (Universita' del Salento, Italy), Mauro Lo Schiavo (Universita' di Roma "La Sapienza", Italy) and Jessica Gronski (UCCS).


References:

1. M. Lo Schiavo, B. Prinari, A.V. Serio, "Analysing quality with generalized kinetic methods", Math. Comp. Mod. *47* (2008) 1150--1166.

2. M. Lo Schiavo, B. Prinari and A.V. Serio, "Mathematical modeling of quality in a medical structure: a case study", Math. Comp. Mod. *54* (2011) 2087--2103.

3. M. Lo Schiavo, B. Prinari, A.J. Gronski, "An artificial neural network approach for modelling the ward atmosphere in a medical unit", submitted (2014).

Sep 29

UB Colloquium
Xuhua He (University of Maryland)
Minimal length elements: some interaction between combinatorics, representation theory, and arithmetic geometry
4:00PM, Mon Sep 29 2014, Math 250

The study of minimal length elements in a conjugacy class of a Weyl group arises in the study of representation theory. Minimal length elements have many remarkable combinatorial properties. The proof, however, is inspired by arithmetic geometry. In the first half of this talk, I will discuss these combinatorial properties, and some stories which lead to the discovery of the proof.

In the second half of this talk, I will talk about some applications of these combinatorial properties to representation theory and arithmetic geometry. I will explain how some ideas in arithmetic geometry lead to new discoveries in representation theory, and vice versa.

Oct 6

Eisenstein series and unitary representations
Date: Monday, Oct 6
4:00PM, Mon Oct 6 2014, Math 250

This talk will be a continuation of my September 8th talk on some joint work with Stephen D. Miller of Rutgers University. We'll describe how square integrability of Eisenstein series, and hence unitarity of representations, reduces to a combinatorial problem that can be checked using a computer.

Oct 13

Algebra Seminar
Michael Rosas (University at Buffalo)
On the Loewy lengths of Specht modules in the principal block of F�3p
4:00PM, Mon Oct 13 2014, Math 250

Attached as PDF

Oct 13

Algebra Seminar
Michael Vaiana (University at Buffalo)
A Modern Approach to Exterior Powers of Irreducible CS_n-modules
4:00PM, Mon Oct 13 2014, Math 250

Attached as a PDF

Oct 20

Algebra Seminar
Moshe Adrian (University of Toronto)
On the local converse problem for GL(n,F)
4:00PM, Mon Oct 20 2014, Math 250

Let F be a non-archimedean local field of characteristic
zero. The local converse problem for GL(n,F) asks to what extent the
twisted gamma factors determine a representation of GL(n,F). Jacquet
has formulated a conjecture on precisely which family of twisted gamma
factors should uniquely determine a representation of GL(n,F). Because
of recent work of Dihua Jiang, Chufeng Nien, and Shaun Stevens, this
conjecture is now settled in many cases. I will report on recent work
to complete the proof of Jacquet's conjecture, joint work with Baiying
Liu, Shaun Stevens, and Peng Xu. I will then report on a refined
version of Jacquet's conjecture in the case of GL(\ell,F), where \ell
is prime. This latter work is joint with Baiying Liu and Geo Kam Tam
Fai.

Oct 24

Geometry & Topology Seminar
Andy Wand (Univ. of Nantes)
Tightness and Legendrian surgery
4:00PM, Fri Oct 24 2014, Math 122

A well known result of Giroux tells us that isotopy classes of contact structures on a closed three manifold are in one to one correspondence with stabilization classes of open book decompositions of the manifold. We will introduce a characterization of tightness of a contact structure in terms of corresponding open book decompositions, and show how this can be used to resolve the question of whether tightness is preserved under Legendrian surgery.

Oct 27

Algebra Seminar
Yiqiang Li (University at Buffalo)
Transfer maps for quantum Schur algebras of classical type
4:00PM, Mon Oct 27 2014, Math 250

I’ll explain how to construct coproducts and transfer maps for the quantum Schur algebras in the geometric Schur duality of classical type.

This is the joint work with Zhaobing Fan.

Oct 28

Applied Mathematics Seminar
Wai-Sun Don (Brown University)
Single Domain Hybrid Fourier Continuation Method and Weighted Essentially Non-oscillatory Finite Difference Scheme for Conservation Law
4:00PM, Tue Oct 28 2014, Math 250

In this talk, we introduce a hybrid Fourier continuation (FC) method and weighted essentially non-oscillatory (WENO) finite difference scheme, together with the high order multi-resolution algorithm by Harten to determine the smoothness of a solution of hyperbolic conservation laws at a given stencil, in a single domain framework (Hybrid), as opposed to in a given subdomain in a multi-domain framework. The Hybrid scheme conjugates an efficient shock-capturing WENO-Z nonlinear scheme in discontinuous stencils with an essentially non-dispersive and non-dissipative linear FC method in smooth stencils, yielding a high fidelity scheme for applications containing both discontinuous and complex smooth structures. Several critical numerical issues in the implementation (such as FFT and Symmetry preserving), accuracy, and efficiency of the Hybrid scheme will be illustrated and resolved. Examples, including the one dimensional classical Riemann IV problems, shock-entropy wave interaction and two dimensional March 3 double Mach reflection problems, regarding the efficiency and accuracy of the Hybrid scheme will be shown.

This is a joint work with Li Peng, Prof. Gao Zhen, and Prof. Xie Shusen during the First Summer Workshop in Advanced Research in Applied Mathematics and Scientific Computing 2013 In the School of Mathematical Sciences at Ocean University of China.

Oct 29

Analysis Seminar
Jingbo Xia (University at Buffalo)
On the membership of Hankel operators in a class of Lorentz ideals
4:00PM, Wed Oct 29 2014, Math 250

Attached as PDF

Nov 3

TBA
Speaker: Dubravka Ban, Southern Illinois University Carbdondale
4:00PM, Mon Nov 3 2014, Math 250

Speaker: Dubravka Ban, Southern Illinois University Carbdondale

Nov 4

UB Math Club- David Hemmer (UB)
Permanents, Determinants and an Introduction to Representation Theory
5:15PM, Tue Nov 4 2014, Math 250

We will give a gentle introduction to the representation theory of finite groups, focusing on the symmetric group. This will lead us naturally to irreducible characters and to generalizations of the determinant of a matrix. These generalizations, called Immanants, are the subject a 50-year old open problem known as the "Permanental-dominance conjecture," which is the subject of active research to this day.

Nov 5

Analysis Seminar
Ron Ji (IUPUI)
Polynomially bounded cohomology and applications
4:00PM, Wed Nov 5 2014, Math 250

Given a clas of weight functions on a discrete group G, one can define a weighted group cohomology. If the weight class is generated by the word length function on a finitely generated group, the cohomology is said to be polynomially bounded cohomology. It can very often happen that this cohomology theory is canonically isomorphic to the regular group cohomology theory. A group is said to be isocohomological if the polynomially bounded cohomology theory is canonically isomorphic to the group cohomology theory. We examine the class of groups satisfying this isocohomologicality condition and many applications of the latter.

Nov 7

Geometry & Topology Seminar
Tarik Aougab (Yale)
Filling pairs with many curves intersecting their union a small number of times
4:00PM, Fri Nov 7 2014, Math 122

We're interested in the following question: fix k>0 and an orientable surface S. Given a pair of simple closed curves (x,y) which fill S, how many curves (simple or possibly with self-intersection) intersect the union of x and y at most k times? In joint work with S. Huang, we showed that for k=1, the filling pairs which maximize this quantity are the minimally intersecting ones. In this talk, we outline a result which shows that the minimally intersecting filling pairs are also close to maximizing this quantity in an asymptotic sense as k approaches infinity. The proof uses an effective version of the Masur-Minsky distance formula derived in joint work with S. Taylor and R. Webb, and also a bit of Teichmuller theory.

Nov 12

Analysis Seminar
Adam Orenstein (SUNY at Buffalo)
Symmetric norming functions and Symmetrically normed ideals
4:00PM, Wed Nov 12 2014, Math 250

There has been an increasing interest in symmetrically-normed ideals in recent years. A widely known example is the Schatten p-class for any p>0. In this talk, the concept of a symmetrically-normed ideal and the related concept of a symmetric norming function will be defined. Some useful properties and theorems, such as Fan's Theorem, will be presented. We will also see some examples besides the Schatten p-classes. After this, the motivation for studying symmetrically-normed ideals will be presented.

Nov 13

Colloquium: Job Candidate
4:00PM, Thu Nov 13 2014, Math 250

Nov 14

Geometry & Topology Seminar
Johanna Mangahas (Buffalo)
Convex cocompact subgroups of right-angled Artin groups
4:00PM, Fri Nov 14 2014, Math 122

I will talk about joint work with Thomas Koberda and Sam Taylor on a version for right-angled Artin groups of convex cocompactness for subgroups of mapping class groups. The latter were defined by Farb and Mosher in partial analogy to convex cocompact hyperbolic manifold groups, and there are interesting connections between all three settings.

Nov 17

Algebra Seminar -- Marcelo Aguiar
Marcelo Aquiar, Cornell
4:00PM, Mon Nov 17 2014, Math 250

Marcelo Aquiar, Cornell

Nov 20

Colloquium: Job Candidate
4:00PM, Thu Nov 20 2014

Nov 24

Colloquium: Job Candidate
4:00PM, Mon Nov 24 2014

Nov 25

Colloquium: Job Candidate
11:00AM, Tue Nov 25 2014, Math 250

Nov 25

Algebra Seminar
Yorck Sommerhäuser (University at Buffalo)
A Triviality Theorem for Yetter-Drinfel'd Hopf Algebras I
4:00PM, Tue Nov 25 2014, Math 250

Usually, a Yetter-Drinfel'd Hopf algebra is not a Hopf
algebra. But if the quasisymmetry in the category of Yetter-Drinfel'd
modules accidentally coincides with the ordinary flip of tensor factors
on the second tensor power of the Yetter-Drinfel'd Hopf algebra, then
the Yetter-Drinfel'd Hopf algebra is indeed an ordinary Hopf algebra.
Such a Yetter-Drinfel'd Hopf algebra is called trivial.

In certain situations, every Yetter-Drinfel'd Hopf algebra is trivial:
As we will prove, a semisimple commutative Yetter-Drinfel'd Hopf algebra
over a finite abelian group is necessarily trivial if its dimension is
relatively prime to the order of the finite abelian group, assuming that
the base field has characteristic zero. The Yetter-Drinfel'd Hopf
algebra therefore must be a dual group ring endowed with some additional
structure.

Nov 26

Start of Fall Recess
Wednesday, November 26, 2014

Dec 1

Classes Resume
Monday, December 1, 2014

Dec 1

A triviality theorem for Yetter-Drinfel'd Hopf algebras II
Speaker: Yorck Sommerhäuser, UB
4:00PM, Mon Dec 1 2014

Speaker: Yorck Sommerhäuser, UB

Dec 2

Colloquium: CDSE Job Candidate
10:00AM, Tue Dec 2 2014, Math 250

Dec 3

Colloquium: CDSE Job Candidate
11:00AM, Wed Dec 3 2014, Math 250

Dec 5

Last Day of Classes
Friday, December 5, 2014

Dec 5

Geometry & Topology Seminar
Nathan Broaddus (Ohio State)
Finite rigid sets and homological non-triviality in the curve complex
4:00PM, Fri Dec 5 2014, Math 122

Go to http://www.acsu.buffalo.edu/~kutluhan/seminar.html

Dec 8

Start of Final Exams
Monday, December 8, 2014

Dec 8

Colloquium: Job Candidate
4:00PM, Mon Dec 8 2014, Math 250

Dec 9

Colloquium: Job Candidate
4:00PM, Tue Dec 9 2014, Math 250

Dec 11

Colloquium: CDSE Job Candidate
10:00AM, Thu Dec 11 2014

Dec 12

Colloquium: CDSE Job Candidate
10:00AM, Fri Dec 12 2014

Dec 15

Last Day of Final Exams
Monday, December 15, 2014

Dec 15

Colloquium: CDSE Job Candidate
10:00AM, Mon Dec 15 2014, Math 250

Jan 14

Spring Semester begins

Monday, January 14, 2013

Jan 21

Martin Luther King, Jr. Day, no classes
Monday, January 21, 2013

Jan 28

Junior Algebra Seminar: David Hemmer
We will be going through the classic book "Young Tableaux" by William Fulton.
4:00PM, Mon Jan 28 2013, 122 Math

We will be going through the classic book "Young Tableaux" by William Fulton.

Feb 4

Junior Algebra Seminar: David Hemmer
4:00PM, Mon Feb 4 2013, Room 122

Feb 8

Geometry/Topology seminars: Bill Menasco
Title:The Kawamuro Cone and the Jones' Conjecture.
4:00PM, Fri Feb 8 2013, Math 122

We will discuss joint work with D. Lafountain on a proof of the Jones'
Conjecture.
Recently, Dynnikov and Prasolov provided a proof of this conjecture. We present
here an alternative approach.

Feb 11

Junior Algebra Seminar: Michael Rosas
Robinson-Schensted-Knuth correspondence
4:00PM, Mon Feb 11 2013, 122 Math

Robinson-Schensted-Knuth correspondence

Feb 13

Analysis Seminar: Lewis Coburn, SUNY at Buffalo
Heat Flow and Uniform Continuity
4:00PM, Wed Feb 13 2013, Math 250

This talk is based on the paper "Heat Flow, weighted Bergman spaces, and real-analytic Lipschitz approximation" by Bauer and Coburn. We examine the spaces of functions of bounded mean oscillation (BMO) on bounded symmetric (Cartan) domains Ω in complex n-space C^n and on Ω = C^n. We show that all β(
;
) (Bergman metric) complex-valued uniformly continuous functions are in BMO(Ω) with some interesting consequences. In particular, all such functions can be uniformly approximated by real-analytic β-Lipschitz functions. The model for our discussion is Ω= C^n, where the heat equation plays a central role in our considerations.

Feb 15

Geometry/Topology Seminar: Pierre Py (University de Strasbourg)
"An exotic deformation of the hyperbolic space."
4:00PM, Fri Feb 15 2013, Math 122

I will explain how to construct a continuous family of “exotic” locally compact CAT(−1) spaces with cocompact isometry groups all isomorphic to the isometry group of the real hyperbolic space H^n. This is joint work with Nicolas Monod.

Feb 19

Applied Mathematics Seminar: Tracy Stepien (University of Pittsburgh)
Collective cell migration in single and multi-layer aggregates
4:00PM, Tue Feb 19 2013, Math 250

Collective cell migration plays an important role in maintaining the cohesion of epithelial cell layers, in wound healing, and in the gastrulation phase of embryonic development. A recently developed continuum mechanical model of the migration of a single cell layer based on an assumption of elastic deformation of the cell layer leads to a generalized Stefan problem. Analysis and numerical results indicate that a large class of constitutive equations for the dependence of proliferation on stretch leads to traveling wave solutions with constant wave speed. The model is extended to describe the migration of two coupled cell layers, and a numerical method based on a level set method for free boundary problems with domain decomposition is constructed.

Feb 22

Geometry/Topology Seminar: Peter Horn (Syracuse University)
"Topologically slice knots, bipolarity, and the Alexander polynomial".
4:00PM, Fri Feb 22 2013, Math 122

Inspired by the Cochran-Orr-Teichner filtration of the
topological knot concordance group, Cochran, Harvey and Horn
introduced the bipolar filtration of the smooth knot concordance
group. The advantage of the bipolar filtration is that questions
about its structure are amenable to techniques from topological and
smooth four manifold theory. In particular, the bipolar filtration
can be used to study the group of (smooth concordance classes of)
topologically slice knots. We will define the filtration, discuss its
relation to known sliceness obstructions, and construct an infinite
family of knots that is interesting within the context of this
filtration and also within the context of Freedman's theorem that
knots with trivial Alexander polynomial are topologically slice.

Feb 25

Geometry/Topology Seminar: Andrew Putman
Rice University
Stability in the homology of congruence subgroups
4:00PM, Mon Feb 25 2013, Math Building Room 122

I'll discuss some recent results which uncover new patterns in the homology groups of congruence subgroups of SLn(Z) and related groups.

Feb 26

Applied Mathematics Seminar: Sara Metcalf, University at Buffalo
Agent-Based System Dynamics: Hybrid Models of Urban Health
4:00PM, Tue Feb 26 2013, Math 250

To address urban health differentials among diverse populations, hybrid models that combine agents with intra- and inter-personal system dynamics enable flexible representation of individuals in urban environments. As the cornerstone of system dynamics, stock and flow structures respond continuously to balancing (negative) and reinforcing (positive) information feedback. In contrast, a different kind of system dynamics involves modeling at the individual level through agents that interact with each other and their environment. Agent-based modeling enables an intuitive heuristic approach to exploring a range of heterogeneous behaviors among agents with dynamic decision rules. Contemporary simulation software enables mixed representation of continuous (stock-flow, differential equation-based) processes and discrete (agent-based) objects, algorithms and events within a single model. Causal maps of feedback loops that signify system dynamics also provide a way to communicate the structural underpinnings of agent-based models and to express dynamic hypotheses that may not be transparent from the model code. Selected examples demonstrate the utility of hybrid implementations of agent-based system dynamics and illustrate their potential for modeling urban health problems.

Mar 4

Junior Algebra Seminar: Michael Vaiana
Littlewood-Richardson Rule
4:00PM, Mon Mar 4 2013, 122 Math

Littlewood-Richardson Rule

Mar 5

Dissertation Defense: Huichi Huang
Compact Quantum Group Actions on Unital C*-algebras
4:00PM, Tue Mar 5 2013, Math 250

Title: Compact Quantum Group Actions on Unital C*-algebras

Mar 7

Math Club: Mohan Ramachandran (University at Buffalo)
In 1798, there appeared in the "Philosophical Transactions of the Royal Society" a paper by James Wood, purporting to prove the fundamental theorem of algebra, to the effect that every non-constant polynomial with real coefficients has at least one real or complex zero. Since the first generally accepted proof of this result was given by Gauss in 1799, Wood's proof deserves careful examination.
4:00PM, Thu Mar 7 2013, Math 250

In 1798, there appeared in the "Philosophical Transactions of the Royal Society" a paper by James Wood, purporting to prove the fundamental theorem of algebra, to the effect that every non-constant polynomial with real coefficients has at least one real or complex zero. Since the first generally accepted proof of this result was given by Gauss in 1799, Wood's proof deserves careful examination.

Mar 8

UB Geometry/Topology Seminar: Prof. Nathan Broaddus (Ohio State)
Homology of the curve complex and the Steinberg module of the mapping class group
4:00PM, Fri Mar 8 2013, Math 122

The homology of the curve complex is of fundamental importance for the cohomology of the mapping class group. It was previously known to be an infinitely generated free abelian group, but to date, its structure as a mapping class group module has gone unexplored. I will give a resolution for the homology of the curve complex as a mapping class group module. From the presentation coming from the last two terms of this resolution I will show that this module is cyclic and give an explicit single generator. As a corollary, this generator is a homologically nontrivial sphere in the curve complex.

Mar 11

Spring Recess begins
Monday, March 11, 2013

Mar 18

Classes resume
Monday, March 18, 2013

Mar 18

Junior Algebra Seminar: David Hemmer
Representation theory and symmetric functions.
8:00AM, Mon Mar 18 2013, 122 Math

Representation theory and symmetric functions.

Mar 19

Applied Mathematics Seminar: moved to April 16 (Abani Patra)
4:00PM, Tue Mar 19 2013

Mar 20

Myhill Lecture: Peter Sarnak, Princeton University
4:00PM, Wed Mar 20 2013, Room 250

Mar 20

Myhill Lecture: Peter Sarnak, Princeton University
Mobius Randomness and horocycle flows at prime times:
4:00PM, Wed Mar 20 2013, Room 250

The Mobius function mu(n) is minus one to the number of prime factors of n, if n has no square factors and is zero otherwise. Understanding the randomness (often called the Mobius randomness principle) in this function is a fundamental and difficult problem. We will explain a precise dynamical formulation of this randomness principle and report on recent advances in establishing it and its applications, especially in connection with a prime number type theorem for horocycle flows.

Mar 21

Myhill Lecture: Peter Sarnak, Princeton University
Thin Matrix Groups and Diophantine Analysis
4:00PM, Thu Mar 21 2013, Room 250

The general Ramanujan Conjectures for congruence subgroups of arithmetic groups and approximations that have been proven towards them are central to many diophantine applications. Recently analogous results have been established for quite general subgroups of GL(n,Z) called "thin groups". We will describe some of these and review their applications as well as the ubiquity of thin groups.

Mar 22

Myhill Lecture: Peter Sarnak, Princeton University
Nodal Lines of Maass forms and critical percolation
4:00PM, Fri Mar 22 2013, Room 250

We describe some results concerning the number of connected components of nodal lines of high frequency Maass forms on the modular surface. Based on heuristics connecting these to a critical percolation model, Bogomolny and Schmit have conjectured, and numerics confirm, that this number follows an asymptotic law. While proving this appears very difficult, some approximations to it can be proved using number theoretic and analytic techniques.This is joint work with A.Ghosh and A.Reznikov .

Mar 25

Algebra Seminar: Adam Sikora (University at Buffalo)
On representations of abstracts groups into Lie groups.
4:00PM, Mon Mar 25 2013, Math 122

We are going to discuss some fundamental questions concerning representations of abstract groups into matrix groups, considered up to conjugation. We will discuss open problems in this area and our work relating it to non-commutative algebra, algebraic geometry, and representation theory of Lie groups.

Apr 9

Applied Mathematics Seminar: Thomas Trogdon (University at Washington)
title: A numerical Riemann--Hilbert approach for the Korteweg--de Vries equation
4:00PM, Tue Apr 9 2013, Math 250

title: A numerical Riemann--Hilbert approach for the Korteweg--de Vries equation

abstract:
It is well known that the Cauchy intial-value problem for the Korteweg--de Vries (KdV) equation on the line may be solved with the inverse scattering transform (IST). Often, the IST is described in terms of the solution of a matrix Riemann--Hilbert problem. Building on this technique, I will describe how the construction of periodic and quasi-periodic solutions of the KdV equation can be performed with matrix Riemann--Hilbert problems. Furthermore, using a computational approach to Riemann--Hilbert problems, the IST, periodic solutions and quasi-periodic solutions are computed with uniform accuracy.

Apr 12

UB Geometry/Topology Seminar: Professor Thang Le (Georgia Institute of Technology)
On the growth of torsions and regulators in finite abelian coverings
4:00PM, Fri Apr 12 2013, Math 122

We discuss the growth of homology of finite coverings, with emphasis on (1) 3-manifolds and (2) abelian coverings of finite CW-complexes.

Apr 15

Junior Algebra Seminar: Yin Su
4:00PM, Mon Apr 15 2013, Math 122

Apr 16

Applied Mathematics Seminar
Abani Patra (UB Mechanical and Aerospace Engineering)
Computational Modeling of Hazardous Mass Flows and Use in Risk Assessment
4:00PM, Tue Apr 16 2013, Math 250

Apr 17

Analysis seminar: Jingbo Xia, SUNY at Buffalo
A Local Inequality for Hankel Operators and its Application
4:00PM, Wed Apr 17 2013, Math 250

. We establish a local inequality for Hankel operators Hf on the Hardy space of the unit sphere in Cn. As an application of this local inequality, we characterize the membership of Hf in the Lorentz-like ideal C+p, 2n

Apr 19

Max Bileschi (SUNY at Buffalo)
An exposition on new results in circuit lower bounds
4:00PM, Fri Apr 19 2013, Davis 203

Title: An exposition on new results in circuit lower bounds

The project will goes over recent research into lower bounds on the computational power of certain classes of circuits. In particular, the results \NEXP\not\subset\ACC and \E^\NP\not\subset\ACC will be examined. Informally, these results give bounds on the computational power of polynomial-size, constant-depth families of circuits. More specifically, the first results says that nondeterministic, exponential-time computations cannot be captured by particular infinite families of polynomial-size digraphs, while the second relates those circuits to deterministic, exponential-time computations, equipped with a particular oracle.

Apr 22

Junior Algebra Seminar: Yin Su
Representation Theory of Symmetric Groups II
4:00PM, Mon Apr 22 2013, 122 Math

Title: Representation Theory of Symmetric Groups II

Apr 24

Analysis seminar: Mira Peterka, University of Kansas
Finitely-generated Projective Modules and Gauge Theory over Theta-deformed Spheres
4:00PM, Wed Apr 24 2013, Math 250

We discuss the classification and construction (up to isomorphism) of the finitely-generated projective modules over the theta-deformed n-spheres of Connes of and Landi. We also review what is known of the gauge theory on these spheres and discuss some open problems and conjectures about the gauge theory.

Apr 29

Last Day of classes!
Monday, April 29, 2013

May 2

Exams begin
Thursday, May 2, 2013

May 3

Johanna Mangahas, Brown University
A "list-and-check" algorithm for Nielsen-Thurston classification
4:00PM, Fri May 3 2013, 122 Math

Fixing a generating set for the mapping class group of a surface, it's easy to see that dilatations grow at most exponentially with word length. Infinite-order, reducible mapping classes have canonical fixed curve sets, and it turns out the lengths of these curves also grow at most exponentially with word length. I'll share a simple computation for such an upper bound, which leads to the algorithm of the title. This is a collaboration with Thomas Koberda.

May 9

Exams end
Thursday, May 9, 2013

May 10

Commencement Weekend
Friday, May 10, 2013

May 20

Summer Session I (J) Begins
Monday, May 20, 2013

May 20

10 Week Sessions (A) Begin
Monday, May 20, 2013

May 20

9 Week Sessions (L) Begin
Monday, May 20, 2013

May 20

12 Week Sessions (I) Begin
Monday, May 20, 2013

May 27

Memorial Day Holiday Observed
Monday, May 27, 2013

Jun 24

Summer Session II (K) Begins
Monday, June 24, 2013

Jun 28

Summer Session I (J) Ends
Friday, June 28, 2013

Jul 1

Summer Session III (M) Begins
Monday, July 1, 2013

Jul 4

Independence Day Holiday Observed
Thursday, July 4, 2013

Jul 19

9 Week Sessions (L) End
Friday, July 19, 2013

Jul 26

10 Week Sessions (A) End
Friday, July 26, 2013

Aug 2

Summer Session II (K) Ends
Friday, August 2, 2013

Aug 9

Summer Session III (M) Ends
Friday, August 9, 2013

Aug 9

12 Week Sessions (I) Ends
Friday, August 9, 2013

Aug 26

Classes Begin
Monday, August 26, 2013

Aug 30

G&T Seminar organizational meeting
4:00PM, Fri Aug 30 2013, Math 122

Sep 2

Labor Day Observed
Monday, September 2, 2013

Sep 4

Rosh Hashanah (Classes Cancelled after 6:00 pm)
Wednesday, September 4, 2013

Sep 5

Classes Resume at 6:00 pm
Thursday, September 5, 2013

Sep 9

Algebra Seminar
Yorck Sommerhäuser (University at Buffalo)
Cauchy's theorem for Hopf algebras
4:00PM, Mon Sep 9 2013, Math 250

Cauchy's theorem states that a finite group contains an element of prime order for every prime that divides the order of the group. Since the exponent of a group is the least common multiple of the orders of all its elements, this can be reformulated by saying that a prime that divides the order of a group also divides its exponent. It was an open conjecture by P. Etingof and S. Gelaki that this result, in this formulation, holds also for semisimple Hopf algebras. In the talk, we present a proof of this conjecture, which is joint work with Y. Kashina and Y. Zhu.

The talk is intended for a general audience; in particular, no knowledge of Hopf algebras will be assumed. We will therefore begin by explaining what a Hopf algebra is and how the exponent of a Hopf algebra can be defined. We will then explain how the analogue of Cauchy's theorem can be deduced from the theory of higher Frobenius-Schur indicators.

Sep 11

Analysis Seminar
Josh Isralowitz (SUNY at Albany)
Compactness of operators on Bergman and Fock spaces.
4:00PM, Wed Sep 11 2013, Math 250

In a deep paper of D. Suárez published in 2007, the classical Axler-Zheng theorem was extended to show that an operator in the Toeplitz algebra of the Bergman space on the unit ball is compact if and only if its Berezin transform vanishes on the boundary. Very recently, a small flurry of results (such as extensions to the Fock space, new essential norm estimates, and vast simplifications of his original proof) have appeared which extend this theorem. In this talk, we will discuss these recent results and the techniques used to prove them. Furthermore, we will discuss some very interesting open problems related to these results. This is partly joint work with Brett Wick and Mishko Mitkovski.

Sep 13

Yom Kippur (Classes cancelled after 6:00 pm)
Friday, September 13, 2013

Sep 13

Geometry & Topology Seminar
Cagatay Kutluhan (Buffalo)
The Seiberg-Witten equations, holonomy filtration, and knots
4:00PM, Fri Sep 13 2013

I will talk about how one can define a doubly filtered chain complex for a null-homologous knot inside a 3-manifold using the Seiberg-Witten equations.

Sep 14

Classes Resume at 6:00 pm
Saturday, September 14, 2013

Sep 20

Geometry & Topology Seminar
Cagatay Kutluhan (Buffalo)
The Seiberg-Witten equations, holonomy filtration, and knots (Continued)
4:00PM, Fri Sep 20 2013

Title: The Seiberg-Witten equations, holonomy filtration, and knots (Continued)

Sep 23

Algebra seminar-- A geometric construction of quantum osp(1/2)
Speaker: Yiqiang Li
4:00PM, Mon Sep 23 2013, Math 250

I'll present a geometric construction of quantum osp(1/2) together with its tensor product modules. I'll discuss a direct connection between various quantum groups which leads to an equivalence of categories of weight modules.

Sep 25

Analysis Seminar
Tim Austin (Courant Institute)
Partial difference equations over compact Abelian groups.
4:00PM, Wed Sep 25 2013, Math 250

Given a compact Abelian group Z, an element z of that group, and a measurable function from it to another such group, one can form a new function by taking the difference of the original function and its translate by z. This is the obvious discrete analog of differentiation, and defines an operator on functions called a differencing operator.

Recent work in additive combinatorics, related to Gowers' proof of Szemerédi's Theorem, leads naturally to the study of certain `higher-order' partial difference equations involving such operators. Given several elements of Z, one asks for a description of those functions on Z which vanish when one applies all of the resulting differencing operators. It turns out that as the order of the difference equation increases, one can sometimes find surprising extra structure among these solutions, which amounts to a first step towards understanding the inverse problem for the `directional Gowers norms'.

Sep 26

Colloquium
John Friedlander (University of Toronto)
The Spin of Prime Ideals
4:00PM, Thu Sep 26 2013, Math 250

We discuss joint work with H. Iwaniec, B. Mazur and K. Rubin. Fixing a nontrivial automorphism of a number field K, we associate to ideals in K an invariant (with values in {0,±1}) which we call the spin. Using techniques from analytic number theory, we show the spin values ±1 occur asymptotically equally often over primes, with a rather sharp error term. We apply the theorem to the arithmetic statistics of the Selmer groups of elliptic curves.

Sep 30

Algebra Seminar
Zhaobing Fan (University at Buffalo)
A unification of Lusztig's modified quantum algebras and their analogues.
4:00PM, Mon Sep 30 2013, Math 250

We show that Lusztig's modified quantum algebras are isomorphic to their analogues associated with two-parameter, multi-parameter algebras and multi-parameter (super)algebras. As a consequence, their weight module categories are equivalent. This is joint work with Yiqiang Li.

Oct 2

Analysis Seminar
Yunping Jiang (CUNY at Queens College & Graduate Center)
Symmetric Invariant Measures and Symmetric Rigidity
4:00PM, Wed Oct 2 2013, Math 250

In the study of modern dynamical systems, an invariant measure is an important topic and in the study of modern complex analysis, the quasisymmetric condition on a map is an important topic. In this talk, I will combine these two topics together introducing a new interesting topic, symmetric invariant measure. I will discuss the existence and the uniqueness of a symmetric invariant probability measure for a uniformly symmetric circle endomorphism. I will also discuss symmetric rigidity related with the uniqueness. I will also discuss the Teichmuller structure and complex manifold structure on the space of symmetric invariant probability measures.

Oct 3

Invitation to Research Colloquium- Bernard Badzioch
Torsion invariants of topological spaces
4:00PM, Thu Oct 3 2013, Math 250

Homology and homotopy groups provide very useful invariants of topological spaces, but since they depend on the homotopy type of the space only they are less useful when one is interested in classifying spaces up to homeomorphism. Torsion invariants help us deal with the issue of distinguishing between spaces that are homotopy equivalent but not homeomorphic. The talk will provide an elementary introduction to the classical theory of torsion invariants. In time permits I will also mention more modern facets of this theory.


Prerequisites:
I will assume that you know some basic material covered in MTH 627:
you should know what is a topological space, CW-complex, fundamental group,
universal covering of a space, homotopy equivalence, chain complex (in particular
cellular chain complex of a CW complex) and its homology.

References:
If you will want to learn more about the subject of the talk here are a couple of very good sources.
The first is a (rather long) paper, the second is a (rather short) textbook:

1) J. Milnor, Whitehead Torsion, Bulleting of the AMS, vol. 72(3), 1966, p. 358-426.
2) M. M. Cohen, A course in simple-homotopy theory, Springer-Verlag 1973.

Oct 4

Geometry & Topology Seminar
Hyungryul Baik (Cornell)
Laminations on the circle and hyperbolic geometry
4:00PM, Fri Oct 4 2013, Math 122

We will see that laminations can be used to study groups acting on the circle. In particular, it is possible to characterize Fuchsian groups in terms of topological invariant laminations. It is a geometrization result in the sense that you start with a topological dynamical data and hyperbolic geometry comes out of the picture. Main motivation of this program is Thurston's universal circle theory for tautly foliated 3-manifolds.

Oct 7

Algebra Seminar
Bin Xu (University of Toronto)
Arthur packet through the trace formula
4:00PM, Mon Oct 7 2013, Math 250

Arthur packets over a local field are finite sets of irreducible
admissible representations of reductive groups. They are important in
the classification of automorphic representations. Although there are
no general definitions for these sets, they come up naturally from the
point of view of Arthur-Selberg trace formula. In the talk I will
first explain this. Then I will give a more detailed description in
the case of symplectic and orthogonal groups, which has been proved by
Arthur. In the end, I will talk about how to go from these classical
groups to their similitude groups, i.e. GSp(2n) and GSO(2n).

Oct 15

Myhill Lectures: Percy Deift (Courant)
Toeplitz matrices and determinants under the impetus of the Ising model I.
4:00PM, Tue Oct 15 2013, Math 250

The first talk will describe the development of Toeplitz theory over the years in response to questions that arose in the analysis of the Ising model in statistical physics. Joint work with Alexander Its and Igor Krasovsky.

Oct 16

Analysis Seminar
Djordje Milicevic (Bryn Mawr College)
Sub-Weyl subconvexity and short p-adic exponential sums
3:00PM, Wed Oct 16 2013, Math 150

One of the principal questions about L-functions is the size of their critical values. In this talk, we will present our recent subconvexity bound for the central value of a Dirichlet L-function of a character to a prime power modulus, which breaks a long-standing barrier known as the Weyl exponent. The results are obtained by developing a new general method to estimate short exponential sums involving p-adically analytic fluctuations, which can be naturally seen as a p-adic analogue of the method of exponent pairs. We will present the main results of this method and the key points in its development, and discuss the structural relationship between the p-adic analysis and the so-called depth aspect.

Oct 16

Myhill Lectures: Percy Deift (Courant)
Toeplitz matrices and determinants under the impetus of the Ising model II.
4:00PM, Wed Oct 16 2013, Math 250

The second talk will follow on from the first, and will describe more technical aspects, together with applications, of the modern theory of Toeplitz matrices. Joint work with Alexander Its and Igor Krasovsky.

Oct 17

Myhill Lectures: Percy Deift (Courant)
Computing the eigenvalues of a random symmetric matrix: Universality properties.
4:00PM, Thu Oct 17 2013, Math 250

The speaker will describe some recent numerical experiments on the computation of the eigenvalues of a random symmetric matrix. Fix an eigenvalue algorithm and choose an ensemble for the matrices: it turns out that the statistics of eigenvalue computation, for a given algorithm, display universality properties, independent of the choice of ensemble. Joint work with Christian Pfrang and Govind Menon.

Oct 21

Algebra seminar
Yorck Sommerhauser (UB)
Introduction to Yetter-Drinfel'd Hopf Algebras I
4:00PM, Mon Oct 21 2013, Math 250

Yetter-Drinfel'd Hopf algebras are Hopf algebras
in a more general category than the category of vector spaces,
namely the category of Yetter-Drinfel'd modules. They appear
in the study of ordinary Hopf algebras at many places, for
example in the analog of the semidirect product construction
or as the "nilpotent" parts of deformed enveloping algebras.
In this way, they have become quite central in contemporary
Hopf algebra theory.

The talk is the first in a small series of talks on the topic. It
requires some modest prior knowledge about Hopf algebras,
but it will not only be directed at experts, and the pace will
be adapted to the audience.

Oct 23

Analysis Seminar
Bingbing Liang (SUNY at Buffalo)
Mean Dimension and von Neumann-Lueck Rank
4:00PM, Wed Oct 23 2013, Math 250

Mean dimension is a numerical invariant in topological dynamics and related to entropy. The von Neumann-Lueck rank is a L^2-invariant and related to L^2 Betti number. I will establish an equality between the von Neumann-Lueck rank of a module of the integral group ring of an amenable group and the mean dimension of the associated algebraic action. Also I will give some applications of this equality. This is a joint work with Hanfeng Li.

Oct 24

Tenured faculty meeting
4:00PM, Thu Oct 24 2013

Oct 25

Geometry/Topology Seminar
Watchareepan Atiponrat (Buffalo)
Title : Rectangular diagrams and Legendrian links
4:00PM, Fri Oct 25 2013, Math 122

: Based on the work of I. Dynnikov and M. Prasolov, rectangular diagrams can be used to study Legendrian links. In our case, we use rectangular diagrams to see when a Legendrian link maximizes the Thurson-Bennequin number within its topological isotopy class.

Oct 28

Algebra Seminar
Wei Ho (Columbia University)
Average sizes of Selmer groups for elliptic curves in families.
4:00PM, Mon Oct 28 2013, Math 250

We discuss results on determining the average size of Selmer groups --
and thereby bounding the average Mordell-Weil rank -- in certain
natural families of elliptic curves over the rational numbers. The
main ideas involve finding explicit descriptions of the relevant
moduli spaces, typically as orbits of representations, and then
counting integral points on them using the geometry of numbers. This
is joint work with Manjul Bhargava.

Oct 30

Analysis Seminar
Yichao Zhang (University of Connecticut)
Vector-Valued and Scalar-Valued Modular Forms
4:00PM, Wed Oct 30 2013, Math 250

Vector-valued modular forms were employed by Borcherds to formulate his theory of automorphic products and other results, but unlike scalar-valued modular forms, they do not possess nice structures. For example, they do not behave well under multiplication. In this talk, we prove an isomorphism between spaces of both kinds of modular forms, generalizing a result of Bruinier and Bundschuh. If time permits, we will describe canonical bases, derive a beautiful duality (Zagier duality), and mention the problem of integrality of Fourier coefficients.

Nov 1

Geometry & Topology Seminar
Steven Sivek (Princeton)
Naturality and contact invariants in sutured monopole homology
4:00PM, Fri Nov 1 2013

Sutured monopole homology is an invariant defined by Kronheimer and Mrowka as a generalization of monopole Floer homology; it assigns a module up to isomorphism to certain 3-manifolds with boundary. In this talk I will explain how to upgrade this invariant from "a module up to isomorphism" to something stronger, explaining why we would care about such naturality questions, and discuss some applications to contact geometry. This is joint work with John Baldwin.

Nov 4

Algebra Seminar Yorck Sommerhauser (UB)
Introduction to Yetter-Drinfel'd Hopf Algebras II
4:00PM, Mon Nov 4 2013, Math 250

While it is possible to form the tensor product of two
Yetter-Drinfel'd modules in a standard way, something unusual
happens when one tries to interchange the two tensor factors:
The usual interchange map between these two tensor products is
neither linear nor colinear. However, there is a replacement
for the interchange map, which, however, is no longer an
involution. To describe this phenomenon, one says that
Yetter-Drinfel'd modules do not form a symmetric category,
but rather a braided category, as this phenomenon is
indeed related to invariants of braids and knots. In the talk,
we will explain these things in greater detail.

Nov 6

Analysis Seminar
Jaehyun Cho (SUNY at Buffalo)
Low-lying zeros of Artin L-functions
4:00PM, Wed Nov 6 2013, Math 250

With Malle's conjecture or a parametric polynomial, we construct families of Artin L-functions. For these families we prove one-level density results unconditionally or under reasonable assumptions. Our results shows that the symmetry type of these families agrees with the symplectic type. This is a joint work with Henry Kim.

Nov 8

Geometry/Topology Seminar
Ki Hyoung Ko (KAIST)
When does a graph braid of index 4 or higher become a right-angled Artin group?
4:00PM, Fri Nov 8 2013, Math 122

We introduce various topological invariants that detect whether a group is a right-angled Artin group or not and we apply them to graph braid groups.

Nov 11

Algebra Seminar- Yorck Sommerhauser (University at Buffalo)
4:00PM, Mon Nov 11 2013, 250 Math

Nov 13

Analysis Seminar
Yoonbok Lee (Rochester University)
Zero-density estimates of L-functions
4:00PM, Wed Nov 13 2013, Math 250

: In the theory of zeta or L- functions it is useful to have good estimates for N(σ, T, 2T), the number of zeros ρ = β+iγ for which β > σ and T< γ < 2T. In this talk we study zero-density estimates of various zeta or L- functions. In particular we introduce that zero-density estimates of a Hecke L-function are related to a universality theorem and fractional moments of the L-function.

Nov 15

Geometry & Topology Seminar
Adam Zarr (Buffalo)
3:00PM, Fri Nov 15 2013

Nov 15

Colloquium: Job Candidate
4:00PM, Fri Nov 15 2013, Math 250

Nov 18

Algebra Seminar Huanchen Bao (University of Virginia)
Schur duality and Kazhdan-Lusztig theory
4:00PM, Mon Nov 18 2013, Math 250

A quantized Schur duality between the quantum group of type A and the Hecke algebra of type A has been discovered by Jimbo in 1986. In this talk we describe a generalization of Schur-Jimbo duality to a duality between a coideal subalgebra of the quantum group of type A and the Hecke algebra of type B. A new theory of canonical basis arising from such a coideal subalgebra is developed which allows a new formulation of Kazhdan-Luszitg theory of type B. As a main application we provide a formulation of Kazhdan-Lusztig theory for the category O of the ortho-symplectic Lie superalgebras for the first time.

Nov 22

Geometry & Topology Seminar
Liam Watson (Glasgow/ICERM)
Khovanov homology and the symmetry group of a knot
3:00PM, Fri Nov 22 2013

This talk will describe an invariant of (appropriately decorated) tangles by considering an natural inverse limit in Khovanov homology. This leads to an invariant of strongly invertible knots, in the form of a graded vector space, that vanishes if and only if the knot is trivial. The invariant appears to contain different information from the Khovanov homology of the knot. For example, it can detect non-amphicheirality in cases where Khovanov homology fails to and separates certain pairs that Khovanov homology does not. More generally, equivalence of strongly invertible knots is best formulated in terms of conjugacy classes of strong inversions in the symmetry goup of a knot, that is, the mapping class group of the knot exterior. This new invariant seems to be quite good at separating these conjugacy classes.

Nov 22

Colloquium: Job Candidate
4:00PM, Fri Nov 22 2013, Math 250

Nov 25

Colloquium: Job Candidate
4:00PM, Mon Nov 25 2013, Math 250

Nov 26

UB Colloquium
Robert Kleinberg (Cornell University)
Group-Theoretic Algorithms for Fast Matrix Multiplication
4:00PM, Tue Nov 26 2013, Math 250

What is the least number of arithmetic operations required to multiply two square matrices? The first two decades of research on this question leveraged identities that expressed trilinear forms related to matrix multiplication as low-rank tensors. An alternative approach, introduced by Cohn and Umans, is based on the theory of finite groups and their group algebras, rather than on trilinear forms. This talk will present the group-theoretic approach to fast matrix multiplication, its successful application using wreath product groups, and a conjecture that would imply the existence of matrix multiplication algorithms with nearly quadratic running time. The subject has appealing connections to additive number theory and to combinatorial constructions of "uniquely solvable puzzles" that are implicit in the work of Coppersmith and Winograd from the 1980's. Joint work with Henry Cohn, Balazs Szegedy, and Chris Umans. The talk will be accessible to undergraduates with some knowledge of finite group theory.

Prof. Kleinberg's visit is sponsored by "URGE to Compute", the Math Dept's NSF-funded undergraduate research program in computational mathematics.

Nov 27

Fall Recess
6:00AM, Wed Nov 27 2013

Dec 2

Classes Resume
Monday, December 2, 2013

Dec 2

Colloquium: Job Candidate
4:00PM, Mon Dec 2 2013, Math 250

Dec 4

Colloquium: Job Candidate
4:00PM, Wed Dec 4 2013

Dec 5

UB Colloquium
Bjorn Sandstede (Brown University)
Localized patterns near onset
4:00PM, Thu Dec 5 2013, Math 250

Many planar spatially extended systems exhibit localized standing structures such as pulses and oscillons. In particular, such structures can emerge at Turing and forced Hopf bifurcations. In this talk, I will give an overview of these mechanisms and show how geometric blow-up techniques can be used to analyze them: among the findings is the bifurcation of localized structures that have significantly larger amplitudes than expected from formal considerations. This is joint work with Kelly McQuighan, David Lloyd, and Scott McCalla.

Dec 6

Last Day of Classes
Friday, December 6, 2013

Dec 7

Reading Days
Saturday, December 7, 2013

Dec 9

Semester Final Examinations
Monday, December 9, 2013

Dec 9

Colloquium: CDSE Job candidate
3:00PM, Mon Dec 9 2013, 250 Math

Dec 10

Colloquium :CDSE Job candidate
4:00PM, Tue Dec 10 2013

Dec 11

Colloquium: CDSE Job Candidate
4:00PM, Wed Dec 11 2013, Math 250

Dec 13

Geometry & Topology Seminar
Eli Grigsby (Boston College)
Khovanov homology and trivial braid detection
4:00PM, Fri Dec 13 2013

I will describe how to use Khovanov homology to detect the trivial braid. The proof is completely combinatorial, relying on an interesting connection between Plamenevskaya's invariant of transverse links and Dehornoy's strict, total order on the braid group. Portions of this talk are joint with John Baldwin, and other portions are joint with Stephan Wehrli.

Dec 16

Colloquium: CDSE Job candidate
4:00PM, Mon Dec 16 2013

Dec 17

Winter Recess Begins
Tuesday, December 17, 2013

Jan 16

Martin Luther King Day Observed
Monday, January 16, 2012

Jan 17

Classes Begin
Tuesday, January 17, 2012

Jan 19

Algebra Seminar
Paul Samuelson (Cornell)
Double affine Hecke algebras and skein modules
4:00PM, Thu Jan 19 2012, Math 250

Title: Double affine Hecke algebras and skein modules

Double affine Hecke algebras were introduced by Cherednik in the early 90's. They are families of algebras associated to root systems, and he used them to prove the Macdonald conjectures, which involve families of symmetric polynomials.

In this talk we describe some applications of the representation theory of double affine Hecke algebras (of type A_1) to skein modules of knot complements. In particular, we show that the skein module of the unknot is a "standard module," and that the skein module of the trefoil is the middle term of a short exact sequence whose first and last terms are twisted standard modules. Most of the talk will be dedicated to a concrete discussion of background and basic facts about the double affine Hecke algebra of type A_1.

Jan 20

Geometry/Topology Seminar
Milena Pabiniak (Cornell University)
Lower bounds for Gromov width in the unitary and special orthogonal coadjoint orbits.
4:00PM, Fri Jan 20 2012, Math 122

Every Lie group acts on the dual of its Lie algebra by the coadjoint action. It is known that the coadjoint orbits of that action are canonically symplectic manifolds. We investigate their Gromov widths using the notion of the Gelfand-Tsetlin system of action coordinates.

Jan 25

Geometry/Topology Seminar
Sang-hyun Kim (KAIST)
Inclusions Between Right-angled Artin Groups
4:00PM, Wed Jan 25 2012, Math 250

Despite their simple presentations, Right-angled Artin groups (RAAGs) are known to have very rich subgroup structures. In particular, we study the question of when there exists an embedding from a RAAG into another RAAG. We give a combinatorial characterization when either (1) the target is two-dimensional, or (2) the source is a three-manifold group. Some interesting consequences are related with surface subgroups and RAAGs defined by cycles.

Key ingredients are Koberda's theorem on groups generated by high-powers of Dehn twists, and the action of pseudo-Anosov maps on the curve complex of a surface. This is ajoint work with Thomas Koberda.

Feb 1

Analysis Seminar
Hanfeng Li (SUNY at Buffalo)
Entropy and L2-torsion, Part I
4:00PM, Wed Feb 1 2012, Math 250

Given any countable discrete group G and any countable left module M of the integral grout ring of G, one may consider the natural action of G on the Pontryagin dual of M. Under suitable conditions, the entropy of this action and the L2-torsion of M are defined. I will discuss the relation between the entropy and the L2-torsion, and indicate how this confirms the conjecture of Wolfang Luck that the universal covering space of any aspherical connected finite CW-complex with nontrivial amenable fundamental group has trivial L2-torsion. This is joint work with Andreas Thom.

Feb 8

Analysis Seminar
Hanfeng Li (SUNY at Buffalo)
Entropy and L2-torsion, Part II
4:00PM, Wed Feb 8 2012, Math 250

Given any countable discrete group G and any countable left module M of the integral grout ring of G, one may consider the natural action of G on the Pontryagin dual of M. Under suitable conditions, the entropy of this action and the L2-torsion of M are defined. I will discuss the relation between the entropy and the L2-torsion, and indicate how this confirms the conjecture of Wolfang Luck that the universal covering space of any aspherical connected finite CW-complex with nontrivial amenable fundamental group has trivial L2-torsion. This is joint work with Andreas Thom.

Feb 13

Colloquium Seminar
Craig Dodge (SUNY Buffalo)
New Results on the Structure of Specht Modules for the Symmetric Group
4:00PM, Mon Feb 13 2012, Math 250

I will give an introduction to the fundamentals of both ordinary and modular representations of finite groups. We will examine examples of representations of the symmetric group both over the complex numbers and an arbitrary field. I will highlight important questions asked by representation theorists, specifically those of interest to mathematicians studying the symmetric group. Finally I will discuss recent contributions made to understanding the homomorphisms between Specht modules andthe structure of Specht modules in characteristic two.

Feb 20

Geometry/Topology Seminar
Laurent Siebenmann (Université de PARIS-SUD)
The famous Poincare Conjecture(s) PC-n viewed from dimension n=2
4:00PM, Mon Feb 20 2012, 122 Math

This is a semi-popular talk that will require modest acquaintance with topological spaces, smooth surfaces, diffeomorphisms, mapping degree, and Euler characteristic. Many students in 3rd year undergraduate mathematics or in 1st year graduate study will hopefully be well prepared.

For any mathematician, there will be some historical and didactic interest. In particular, I will give a (conjecturally) new elementary proof of PC-2, for which Henri Poincare had discovered the techniques, but which, for some reason, he never gave. I will also mention several other proofs. In particular, a very recent proof of PC-2 based on "Ricci flow", the highly sophisticated analytic method of R.S. Hamilton, using which G. Pereleman and his followers have, in this century, conquered the 3-dimensional Poincare Conjecture PC-3.

Feb 22

Analysis Seminar: Invariant subspaces for certain finite-rank perturbations of diagonal operators. Speaker: Jingo Xia
4:00PM, Wed Feb 22 2012, Room 250

Feb 22

Applied Math Seminar
Emmanuel Lorin (Carleton University)
Nonlinear Optics: Modeling, Analysis& Simulation in Some Extreme Regimes
4:00PM, Wed Feb 22 2012, Math 122

In this talk we are interested in the modeling and simulation of intense and ultrashort electromagnetic fields propagating in a molecular gas. In this goal a Maxwell-Schroedinger system has been proposed in [1] and improved in [2]. The electromagnetic field (laser pulse) is modeled by the macroscopic Maxwell equations which are coupled with many time dependent Schroedinger equations using a P.I.C.-like approach. The ab initio description of the laser-molecule interaction allows us to include high order harmonics and nonlinearities. When the gas is ionized, a plasma of free electrons is created inducing a current whose evolution is modeled by a differential equation which is coupled with the Maxwell-Schroedinger system. After discussing some mathematical properties of this system, and its numerical approximation and optimization, we will present some simulations. In particular, ab-initio self-focusing and defocusing effects will be observed and discussed.

[1] E. Lorin, S. Chelkowski, A. Bandrauk. A numerical Maxwell-Schroedinger model for laser-matter interaction and propagation, Comput. Phys. Comm., 177 (12), 2007.

[2] E. Lorin, S. Chelkowski, A. Bandrauk. The WASP model: A micro-macro system for Wave-Schroedinger-Plasma equations, Commun. Comput. Phys., 9(2), 2011

Feb 24

Geometry/Topology Seminar
Jason DeBlois (University of Pittsburgh)
Tessellations of hyperbolic surfaces
4:00PM, Fri Feb 24 2012, 122 Math

A discrete set S in the plane canonically determines a Delaunay tessellation, a decomposition into convex polygons such that each has its vertices in S and is inscribed in a circle containing no other points of S. For some sets there are Delaunay polygons with "large aspect ratio" -- circumcircle radius much larger than some or all of their edge lengths -- and this may obstruct extracting geometric information about S from its Delaunay tessellation. In this talk I will describe a way of surmounting the aspect ratio problem by coarsening the tessellation and, time permitting, give some applications to the geometry of closed hyperbolic surfaces.

Feb 29

Analysis Seminar- Huichi Huang (SUNY Buffalo)
Faithful compact quantum group actions on connected compact metrizable spaces
4:00PM, Wed Feb 29 2012, Room 250

All known (commutative) compact spaces admitting genuine faithful compact quantum group actions are disconnected. Goswami showed that there is no genuine faithful quantum isometric action of compact quantum groups on the Riemannian manifold G/T where G is a compact, semisimple, centre-less, connected Lie group with a maximal torus T and conjectured that the quantum permutations on (disconnected) finite sets are the only possible faithful actions of genuine compact quantum groups on classical spaces. We construct faithful actions of quantum permutation groups on connected compact metrizable spaces and disprove Goswami's conjecture.

Mar 2

Geometry/Topology Seminar
William Menasco (SUNY Buffalo)
The Dehornoy floor and the Markov Theorem without Stabilization
4:00PM, Fri Mar 2 2012, Math 122

The Markov Theorem without Stabilization (MTWS) [Birman-M] tells us that for a fixed braid index n there are a finite number of ``modelled'' isotopes (dependent only on n) which take any closed n-braid immediately to a representative of minimal index. Once at minimal index there is a finite number of modelled isotopes (again, dependent only on the value of the braid index) that allows one to jump between conjugacy classes of minimal index. These isotopes which will grow in number as n grows make up the MTWS calculus for closed braids. Connections between the Dehornoy floor and isotopes of the MTWS calculus were first made by T. Ito. In this talk we will expand on these connections by showing a new characterisation of MTWS isotopes for braids. This talk will feature joint work with Doug Lafountain [Aarhus University] & Hiroshi Matsuda [Yamagata University].

Mar 7

Analysis Seminar: Anthony Weston (Canisius College)
Ultrametrics
4:00PM, Wed Mar 7 2012, Room 250

Mar 9

Geometry/Topology Seminar
Dror Bar-Natan (University of Toronto)
Meta-Groups, Meta-Bicrossed-Products, and the Alexander Polynomial
4:00PM, Fri Mar 9 2012, 122 Math

. A straightforward proposal for a group-theoretic invariant of knots fails if one really means groups, but works once generalized to meta-groups (to be defined). We will construct one complicated but elementary meta-group as a meta-bicrossed-product (to be defined), and explain how the resulting invariant is a not-yet-understood generalization of the Alexander polynomial, while at the same time being a specialization of a somewhat understood "universal finite type invariant of w-knots" and of an elusive "universal finite type invariant of v-knots".

Mar 12

Spring Recess
Monday, March 12, 2012

Mar 19

Dissertation Defense, Phu N. Chung
Homoclinic Groups, Expansive Algebraic Actions, and Actions of Sofic Groups.
4:00PM, Mon Mar 19 2012, Room 250

Title: Homoclinic Groups, Expansive Algebraic Actions, and Actions of Sofic Groups.

Advisor: Dr. H. Li, Committee Members: Dr. C. Chou, Dr. L. Coburn

Mar 29

Colloquium Talk: Vitaly Bergelson (Ohio State University)
Uniform distribution, generalized polynomials and dynamical systems
4:00PM, Thu Mar 29 2012, 250 Math

A classical theorem due to H. Weyl states that if P is a polynomial over R such that at least one of its coefficients (other than the constant term) is irrational, then the sequence P(n), n=1,2,... is uniformly distributed mod 1. We will discuss some recent extensions of this theorem which involve "generalized polynomials", that is, functions which are obtained from the conventional polynomials by the use of the greatest integer function, addition and multiplication. We will explain the role of dynamical systems in obtaining these results and discuss some of the connections with and applications to combinatorics and number theory.

Apr 2

Dissertation Defense, Alyssa Brown
Cubic Rotation Symmetric Boolean Functions.
4:00PM, Mon Apr 2 2012, Room 250

Title: Cubic Rotation Symmetric Boolean Functions.

Advisor: Dr. T. Cusick, Committee Members: Dr. M. Cowen, Dr. D. Hemmer

Apr 6

Dissertation Defense, Craig Dodge
Modular Representations of the Symmetric Group: Structure of Specht Modules.
4:00PM, Fri Apr 6 2012, Room 250

Title: Modular Representations of the Symmetric Group: Structure of Specht Modules.

Advisor: Dr. D. Hemmer, Committee Members: Dr. B. Badzioch, Dr. Y. Li

Apr 10

Grady Wright (Boise State University)

4:00PM, Tue Apr 10 2012, Rm 250

Kernel methods such as those based on radial basis functions (RBFs) are becoming increasingly popular for numerically solving partial differential equations (PDEs) because they are geometrically flexible, algorithmically accessible, and can be highly accurate. There have been many successful applications of these techniques to various types of PDEs defined on planar regions in two and higher dimensions, and more recently to PDEs defined on the surface of a sphere. In this talk we describe a kernel method based on RBFs for numerically solving PDEs defined on more general surfaces, specifically on smooth surfaces embedded in R^3 with no boundary. We describe the accuracy and stability of the method and its application to certain biologically relevant, non-linear reaction diffusion equations on various surfaces.

Apr 11

Analysis Seminar, Wenming Wu, Chongqing Normal University
Uncertainty principles for infinite abelian groups
4:00PM, Wed Apr 11 2012, Rm 250

There are different uncertainty principles in quantum mechanics and mathematics. In this talk, by using the projections, I will use the operator theory to revisit the uncertainty principle on finite cyclic groups and to discuss the uncertainty principle on the group Z. This is joint work with Liming Ge, Jinsong Wu, and Wei Yuan.

Apr 13

Geometry/Topology Seminar
Ian Biringer (Yale)
Random samplings of locally symmetric spaces
4:00PM, Fri Apr 13 2012, Math 122

Suppose that Mi is a sequence of closed locally symmetric spaces modeled on a fixed symmetric space X, e.g. a sequence of hyperbolic n-manifolds. We introduce a tool to understand how the geometry of Mi near a random sample point develops as i tends to infinity. Applications include a control on the growth of the Betti numbers of Mi when X has higher rank.

Apr 16

Dissertation Defense, Debananda Chakraborty
Title is: Spectral and Weno Methods for Hyperbolic PDEs with Singular Source Term.
4:00PM, Mon Apr 16 2012, Room 250

Title is: Spectral and Weno Methods for Hyperbolic PDEs with Singular Source Term.

Advisor: Dr. J. Jung, Committee Members: Dr. J. Ringland, Dr. B. Spencer, Dr. G. Biondini

Apr 17

Myhill Lecture Series
Mladen Bestvina (University of Utah)
Topology of Numbers
4:00PM, Tue Apr 17 2012, 250 Math

The first half of the talk will be a review of how to solve, following Conway, equations such as x^2-2*y^2=6 over the integers. Roughly speaking, one enters a number (value of the form) in a few complementary components of the SL(2,Z) spine (=topograph) in hyperbolic plane, and the solutions appear. Positive and negative values are separated by a line (=river), which is the axis of the symmetry group. The second half of the talk will sketch a generalization of this to hyperbolic 3-space, corresponding to integral binary hermitian forms. The topograph becomes the spine of the suitable Bianchi group, and the river becomes an ocean (a copy of hyperbolic plane). This is joint work with Gordan Savin.

Apr 18

Myhill Lecture Series
Mladen Bestvina (University of Utah)
Topology and geometry of Out (F_n)
4:00PM, Wed Apr 18 2012, 250 Math

The study of Out(F_n), the group of outer automorphisms of the free group F_n of rank n, began by Nielsen in the 1920's. It reached the modern era in the 1980's when Culler and Vogtmann introduced Outer space, a contractible space on which Out(F_n) acts properly discontinuously. More recently, metric properties of Outer space have become a focus of study, giving simpler proofs of old results and opening doors to new. The talks will emphasize analogies with mapping class groups and Teichmuller theory.

Apr 19

Myhill Lecture Series
Mladen Bestvina (University of Utah)
Topology and geometry of Out (F_n)
11:00AM, Thu Apr 19 2012, 250 Math

The study of Out(F_n), the group of outer automorphisms of the free group F_n of rank n, began by Nielsen in the 1920's. It reached the modern era in the 1980's when Culler and Vogtmann introduced Outer space, a contractible space on which Out(F_n) acts properly discontinuously. More recently, metric properties of Outer space have become a focus of study, giving simpler proofs of old results and opening doors to new. The talks will emphasize analogies with mapping class groups and Teichmuller theory.

Apr 20

(postponed
date TBA) Dissertation Defense, Garry Halliwell
postponed to Fri 5/4/12
3:30PM, Fri Apr 20 2012

postponed to Fri 5/4/12

Apr 25

Analysis Seminar
Ben Steinhurst, Department of Mathematics, Cornell University
Spectral Analysis and Dirichlet forms on Barlow-Evans Fractals
4:00PM, Wed Apr 25 2012, Math 250

I will construct a class of metric measure spaces starting from base metric measure spaces each with a Dirichlet form. The Dirichlet form on the chosen base space can then be extended to the limit space. Of particular interest is that when the construction is performed with reasonable choices of parameters and full description of the spectrum of the Laplacian associated to the limiting Dirichlet form is possible. I will give a brief overview of what has been possible to calculate using the spectrum of a particularly simple example of this construction.

Apr 26

Dissertation Defense, Xinjuan Chen
The Inverse Reconstruction of Basis and Frames.
12:00PM, Thu Apr 26 2012, Room 122

Title: The Inverse Reconstruction of Basis and Frames.

Advisor: Dr. J. Jung Committee Members: Dr. B. Pitman and Dr. K. Hoffmann

Apr 26

Mathematics Colloquium
Jesse Peterson, Vanderbilt University
W*-superrigidity
4:00PM, Thu Apr 26 2012, Math 250

Given a free, measure preserving action of a countable group on a probability space, Murray and von Neumann constructed a finite von Neumann algebra known as the group-measure space construction. Properties of this von Neumann algebra reflect properties of the group action, but in general much of the information about the group action is lost. For instance, a seminal result of Connes shows that any two free, ergodic actions of infinite amenable groups give rise to the same von Neumann algebra. Recently, examples of group actions have been found such that the group-measure space construction completely remembers the group and the action. Such actions are termed W*-superrigid, we will present an overview of results in this direction.

Apr 30

Last Day of Classes
Monday, April 30, 2012

May 3

First Day of Final Exams

Thursday, May 3, 2012

May 10

Last Day of Final Exams

Thursday, May 10, 2012

May 11

Commencement Weekend

Friday, May 11, 2012

May 21

Summer Session I (J) begins

Monday, May 21, 2012

May 28

Memorial Day (No classes)

Monday, May 28, 2012

Jun 29

Summer Session I (J) ends

Friday, June 29, 2012

Jul 2

Summer Session III (M) begins

Monday, July 2, 2012

Jul 4

Independence Day (No classes)

Wednesday, July 4, 2012

Aug 10

Summer Session III (M) ends

Friday, August 10, 2012

Aug 27

Fall Semester Begins

Monday, August 27, 2012

Sep 3

Labor Day (No classes)

Monday, September 3, 2012

Sep 5

Analysis Seminar: Yunhua Zhou (Chongqing University)
Quasi-Shadowing property for partially hyperbolic diffeomorphisms
4:00PM, Wed Sep 5 2012, 250 Math Bldg

It is well known that an Anosov diffeomorphism has the shadowing property. However, we can not expect that in general the shadowing property holds for a partially hyperbolic diffeomorphism because of the existence of the center direction. In this talk, I will introduce the quasi-shadowing property for partially hyperbolic diffeomorphisms.In fact, it is showed that for any pseudo orbit {xk}, there is a sequence of points {yk} tracing it in which yk+1 is obtained from f(yk) by a motion along center direction. I will also discuss some applications of this quasi-shadowing property.

Sep 7

Geometry/Topology Seminar: Owen Baker (McMaster)
Cannon-Thurston Maps
4:00PM, Fri Sep 7 2012, Math 122

Gromov defined a class of groups called hyperbolic groups and associated a
boundary space to each. A question arises: if H is there always a natural map from the boundary of H to that of G? Such a
map, when well-defined, is called a Cannon-Thurston map after a family of
examples constructed by Cannon and Thurston. In this talk, I will discuss
joint work with Tim Riley where we answer the question in the negative.
Time permitting, I will talk about connections with subgroup distortion.

Sep 10

Yiqiang Li
Beyond Springer correspondence of type A.
4:00PM, Mon Sep 10 2012, Room 250 Math Building

I'll talk about a generalization of Springer correspondence of type A by introducing a class of simple perverse sheaves on framed representation varieties of Jordan quiver. Its relationship with representation theory of symmetric groups and Schur algebras with be discussed.

Sep 12

Analysis Seminar: Nikolai Vailevski (CINVESTAV, Mexico City)
Two-dimensional singular integral operators via poly-Bergman spaces,
4:00PM, Wed Sep 12 2012, 250 Mathematics Bldg

We describe a direct and transparent connection between the
poly-Bergman type spaces on the upper half-plane and the action of the
certain two-dimensional singular integral operators.

We study then the C*-algebra generated by Toeplitz operators acting on
the Bergman space over the unit disk, whose pseudodifferential defining
symbols belong to the algebra generated by the multiplication operators
and the above two-dimensional singular integral operators (considered
in the unit disk setting). As it turns out this Toeplitz algebra
coincides with the algebra generated by Toeplitz operators with just
functional symbols. At the same time, the generating Toeplitz operators
for above two algebras possess quite different properties.

Sep 14

Geometry/Topology Seminar: Mohan Ramachandran (University at Buffalo)
On Shafarevich's Conjecture
4:00PM, Fri Sep 14 2012, Math 250

Title: On Shafarevich's Conjecture

Sep 16

Rosh Hashanah (classes cancelled from 6pm Sun 9/16
6pm Mon 9/17)

6:00PM, Sun Sep 16 2012

Sep 20

Colloquium: Klaus Schmidt (University of Vienna and Erwin Schrödinger Institute)
Sandpiles and the Harmonic Model
4:00PM, Thu Sep 20 2012, Math 250

The critical sandpile model was introduced by Bak, Tang and Wiesenfeld in 1987–88 and attracted a lot of attention after the discovery of a somewhat elusive abelian group structure of this lattice model by Deepak Dhar. In this lecture I will discuss some connections between sandpiles, the classical spanning tree and dimer models, and the harmonic model (a Z^2-action by automorphisms of a compact abelian group). One of these connections is that all these models have identical entropies.

I will show that the sandpile model is an equal entropy symbolic cover of the harmonic model, which explains some of the algebraic features of the sandpile model.

This is joint work with Evgeny Verbitskiy.

Sep 21

Geometry/Topology Seminar: Jason Manning (UB)
TITLE: The virtual Haken conjecture, I
4:00PM, Fri Sep 21 2012, Math 122

I'll give an overview of the virtual Haken conjecture and
some of the breakthroughs which have led to a proof. In future
seminars, I'll outline Agol's proof in more detail, and talk about
joint work between Agol, Groves, and myself which is used in the
proof.

Sep 25

Analysis Seminar: Piotr Hajac (Institute of Mathematics of the Polish Academy of Sciences and Warsaw University)
The K-theory of Heegaard quantum lens spaces
4:00PM, Tue Sep 25 2012, Math 250

Representing Z/NZ as roots of unity, we restrict a natural U(1)-action on the Heegaard quantum sphere to Z/NZ, and call the quotient spaces Heegaard quantum lens spaces. Then we use this representation of Z/NZ to construct an associated complex line bundle. The main result is the stable non-triviality of these line bundles over any of the quantum lens spaces we consider. We use the pullback structure of the C*-algebra of the lens space to compute its K-theory via the Mayer-Vietoris sequence, and an explicit form of the odd-to-even connecting homomorphism to prove the stable non-triviality of the bundles.

Sep 25

Yom Kippur (classes cancelled 6pm Tue 9/25
6pm Wed 9/26)

6:00PM, Tue Sep 25 2012

Sep 28

Geometry/Topology Seminar: Moon Duchin (Tufts)
Sprawl
4:00PM, Fri Sep 28 2012, Math 122

I'll introduce a statistic that measures the presence of shortcuts in the large-scale geometry of a group or space; having no shortcuts, on average, is thought of as "statistical hyperbolicity." Beginning in the world of finitely generated groups or geometric topology, one is in either case led in an interesting way through convex geometry. I will survey some existing work and pose some open questions.

Oct 2

Applied Mathematics Seminar: Tony Mastroberardino (Penn State Erie)
On the limitations of Kummer's function in heat transfer problems
4:00PM, Tue Oct 2 2012, Math 250

The study of two-dimensional boundary layer flow over a moving surface in a fluid at rest was initiated by Sakiadis. Crane extended the work of Sakiadis by obtaining an exact analytical solution for the case of a linearly stretching surface. In regard to several recent studies that incorporate a viscoelastic fluid and heat transfer analysis, I will demonstrate that the reported solutions of the thermal energy equation given in terms of Kummer's function do not converge at the boundary, and therefore, the values of the wall temperature gradient and wall temperature for the two general types of non-isothermal boundary conditions are incorrect. In contrast I will show that the homotopy analysis method (HAM) provides accurate values of the relevant boundary derivatives via a graphical and numerical demonstration of convergence.

Oct 3

Analysis Seminar: Jingbo Xia (SUNY at Buffalo)
Localization and Berezin Transform on the Fock space
4:00PM, Wed Oct 3 2012, Math 250

We introduce the class of sufficiently localized operators on the Fock space. This class contains many familiar operators, including all the Toeplitz operators with bounded symbols. We show that if A is in the C*-algebra generated by the class of sufficiently localized operators and if the Berezin transform of A vanishes at infinity, then A is compact. The main point of this work is that this compactness is a consequence of a very simple inequality derived from a classic idea that dates back to the 1970s. This is joint work with Dechao Zheng.

Oct 5

Geometry/Topology Seminar: Mohan Ramachandran
On fundamental groups of complete Kaehler manifolds
4:00PM, Fri Oct 5 2012, Math 122

Title: On fundamental groups of complete Kaehler manifolds

Oct 8

Algebra Seminar: Stephen Doty (Loyola University Chicago)
TITLE: Generalized q-Schur algebras
4:00PM, Mon Oct 8 2012, Math 250

Generalized q-Schur algebras are q-deformations of certain finite dimensional algebras (the generalized Schur algebras) introduced by S. Donkin in the late 1980s in order to study the representation theory of reductive algebraic groups. I will summarize some of the historical background and outline a recent approach to these algebras via generators and relations (joint work with Tony Giaquinto) which provides a new (elementary) proof that they are quasihereditariy in all specializations over a field, including the root of unity case.

Oct 10

Analysis Seminar: Xin Li (University of Munster)
Semigroup C*-algebras and their K-theory
4:00PM, Wed Oct 10 2012, Math 250

We compute K-theory for semigroup C*-algebras. In a more general context, we obtain a K-theoretic formula for crossed products attached to certain dynamical systems on totally disconnected spaces. This is joint work with J. Cuntz and S. Echterhoff.

Oct 15

Applied Mathematics Seminar: Sung Ha Kang (Georgia Tech)
Mathematical approaches to Image Colorization and Segmentation.
4:00PM, Mon Oct 15 2012, Math 150

This talk will start with an introduction to image processing, from a well-known Total Variation minimizing denoising. The talk will consider image inpainting problem and colorization. The term ``colorization'' was introduced by Wilson Markle who first processed the gray scale moon image from the Apollo mission. This term was used to describe the process of adding color to grayscale movies or TV broadcasting program. Couple of variational colorization models will be presented which demonstrates different effects. Another direction of using Reproducing Kernel Hilbert Space approach will be presented for an effective colorization application. A link to image segmentation will be made through medical image application.

Oct 15

Algebra Seminar: Dr. Zhaobing Fan (University at Buffalo)
Mixed perverse sheaves and two-parameter quantum groups
4:00PM, Mon Oct 15 2012, Math 250

We give a geometric realization of the negative part of two-parameter quantum groups by using perverse sheaves and
Deligne's weight theory. The canonical basis is constructed. This is joint work with Yiqiang Li.

Oct 17

Analysis Seminar: Sheng-Chi Liu (Texas A&M University)
Subconvexity and equidistribution of Heegner points in the level aspect
4:00PM, Wed Oct 17 2012, Math 250

We will discuss the equidistribution property of Heegner points of level q and discriminant D, as q and D go to infinity. We will establish a hybrid subconvexity bound for certain Rankin-Selberg L-functions which are related to the equdistribution of Heegner points. This joint work with Riad Masri and Matt Young.

Oct 19

Geometry/Topology Seminar: Jason Manning (UB)
The virtual Haken conjecture, II
4:00PM, Fri Oct 19 2012, Math 122

Title: The virtual Haken conjecture, II

Oct 22

Algebra Seminar: Han Li (Yale University)
Effective Discreteness of the 3-dimensional Markov Spectrum
4:00PM, Mon Oct 22 2012, Math 250

Let O=non-degenerate, indefinite, real quadratic forms in 3-variables. For every quadratic form Q in the set O, we define the Markov infimum m(Q)=inf{|Q(v)|^3/|det Q|: v is a non-zero integral vector in R^3}. The set M={m(Q): Q is in O} is called the 3-dimensional Markov spectrum. An early result of Cassels-Swinnerton-Dyer combined with Margulis' proof of the Oppenheim conjecture asserts that, M \intersect (a, \infty) is a finite set for every a>0. In this lecture we will show that #{M \intersect (a, \infty)}<
This is a joint work with Prof. Margulis, and our method is a combination of dynamics on homogeneous spaces, geometry of numbers and automorphic representations.

Oct 23

Applied Mathematics Seminar: Ling Bian (UB)
A Social Network Model to Simulate Transmission of Communicable Diseases
4:00PM, Tue Oct 23 2012, Math 250

Communicable diseases are transmitted from individual to individual following a network of contacts in a population. Through this network, diseases spread across space and time. Reports on some of the most dangerous communicable diseases, such as SARS and H1N1 flu, have repeatedly stressed the importance of individuals in disease transmission. Individual-based disease modeling, however, is still in its infancy and faces many challenges. This presentation discusses the conceptual framework, design, and implementation for modeling the spatial and temporal heterogeneity in the transmission of communicable diseases. The conceptual framework explores a three-population (daytime, nighttime, and pastime population) and three-scale (individual, local, and societal scale) social network. An individual-based and spatially explicit design helps represent heterogeneous, mobile, interacting individuals and their individualized vulnerability to infection. A simulation of individuals’ vulnerability to influenza in an urban area in the Northeastern United States is used to illustrate the proposed framework and design. Simulation results correspond well to the reported epidemic information. The findings offer a valuable platform to devise spatially and temporally oriented control and intervention strategies for communicable diseases.

Oct 26

Geometry/Topology Seminar: Kathryn Mann, University of Chicago
The group structure of diffeomorphism groups
4:00PM, Fri Oct 26 2012, Math 122

What is the relationship between manifolds and the structure of their diffeomorphism groups?
On the positive side, a remarkable theorem of Filipkiewicz says that the group structure determines the manifold: if Diff(M) and Diff(N) are isomorphic, then M and N are diffeomorphic. On the negative side, we know little else. Could the group Diff(M) act by diffeomorphisms on M in nonstandard ways? Does the "size" of Diff(M) say anything about the complexity of M? Ghys asked if M and N are manifolds, and the group of compactly supported diffeomorphisms of N injects into the group of compactly supported diffeomorphisms of M, can the dimension of M be less than dim(N)? We'll discuss these and other questions, and answer these in the (already quite rich) case of dim(M)=1.

Oct 30

Applied Mathematics Seminar: Puneet Singla (UB)
Uncertainty Propagation for Nonlinear Dynamical Systems
4:00PM, Tue Oct 30 2012, Math 250

The main difficulty in the understanding of complex physical dynamic systems is due to uncertainties in the models and measurements. These systems are often studied via numerical simulations with very high dimensional input parameter space. The most critical challenge here is to provide a quantitative assessment of how closely these simulations reflect reality in the presence of model uncertainty, discretization errors, as well as measurement errors. These issues affect the way in which models are constructed, how models are used for performance analysis, and how data is integrated with models for prediction.

This talk will focus on recent development of mathematical and algorithmic fundamentals for uncertainty characterization, forecasting, and data assimilation for nonlinear systems. The central idea is to replace evolution of initial conditions for a large dynamical system by evolution of probability density functions (pdf) for state variables. The use of Fokker-Planck-Kolmogorov equation (FPKE) and Chapman-Kolmogorov equation (CKE) to determine evolution of state pdf due to probabilistic uncertainty in initial or boundary conditions, model parameters and forcing function will be discussed. By accurately characterizing the uncertainty associated with both process and measurement models, this work offers systematic design of low-complexity data assimilation algorithms with significant improvement in nominal performance and computational effort. The applicability and feasibility of these new ideas will be demonstrated on benchmark problems and some real world problems such as tracking resident space objects and forecasting volcano ash footprints.

Oct 31

Analysis Seminar: Steve Lester (University of Rochester)
The distribution of values of the Riemann zeta-function
4:00PM, Wed Oct 31 2012, Math 250

In his 1859 paper "On the Number of Primes Less Than a Given Magnitude," Riemann provided an argument that showed why the distribution of the prime numbers should be related to the zeros of a function of a complex variable. Riemann denoted this function by zeta(s) and made five conjectures about its properties. All but one of these conjectures has been proved. The conjecture that has not been proved (or disproved) is known as the Riemann Hypothesis and states that all the non-real zeros of zeta(s) lie on the line Re(s) = 1/2.

In this talk we will look at the problem of understanding the distribution of the points s at which zeta(s) = a, where a is a non-zero complex number. These points are known as a-points and have long been an object of study. We will discuss many of the known properties of a-points and how these properties compare to those of zeros of zeta(s). Additionally, we will describe recent joint work of ours with Steve Gonek and Micah Milinovich on simple a-points and also discuss the problem of determining how many a-points lie on the line Re(s) = 1/2.

Nov 2

Geometry/Topology Seminar: William Menasco (UB)
The curve complex has dead ends
4:00PM, Fri Nov 2 2012, Math 122

Let X,Y be vertices in in the curve complex C of a non-exceptional surface. The vertex Y is a dead end with respect to X if there is no extension of geodesics joining X and Y, past Y, to longer geodesics. It has a double dead end if it has dead ends at both X and Y. We will discuss what has apparently been missed: that there are myriad examples of dead ends and double dead ends in C, the simplest example being one in which d(X,Y)=3 on a surface of genus 2. (This is joint work with Joan Birman.)

Nov 5

URGE Special Seminar: Robert Harrison (Stony Brook University)
Seeking a sustainable model for scientific simulation
4:00PM, Mon Nov 5 2012, Math 250

Many are now questioning whether our current approaches to developing software for science and engineering are sustainable. In particular, can we deliver to society and the nation the full benefits expected from high-performance simulation at the peta and exascales? Or is innovative science being stifled by the increasing complexities of all aspects of our problem space (rapidly changing hardware, software, multidisciplinary physics, etc.)?

Focusing on applications in chemistry and materials science, and motivated co-design of exascale hardware and software, I will discuss many of these issues including how chemistry has already been forced to adopt solutions that differ quite sharply to those in the mainstream, and how these solutions position us well for the technology transitions now under way. Radical changes in how we compute, going all the way back to the underlying numerical representation and algorithms used for the simulation, also promise great enhancements to both developer productivity and the accuracy of simulations.

Nov 13

Applied Mathematics Seminar: Austin Anuta-Darling (UB)
Chaotic Dynamics in a Model of Traveling-Wave Electrophoresis
4:00PM, Tue Nov 13 2012, Math 250

Traveling-wave electrophoresis is currently being investigated as an improvement upon standard capillary electrophoresis. While capillary electrophoresis mobilizes ions in a microfluidic channel using a static and uniform electric field, traveling-wave electrophoresis utilizes an inter-digitated electrode array along a microfluidic channel to produce a traveling wave of electric potential. The frequency and amplitude of this traveling-wave can then be tuned in order to selectively mobilize ions in the channel with desired characteristics.
This talk will discuss the development of a 2-dimensional model of traveling-wave electrophoresis and the analysis of computer simulations of the model. The analysis of the 2-dimensional model shows that ion motions can exhibit mode-locking, chaos, and quasiperiodicity. The chaotic dynamics are studied in more detail using Lyapunov exponents, bifurcation diagrams, and winding-numbers in the form of average ion velocities. These simple tools alone reveal a significant amount of intricacy and complexity present in the ion trajectories.

Nov 14

Analysis seminar: Huichi Huang (SUNY at Buffalo)
Invariant subsets under compact quantum group actions
4:00PM, Wed Nov 14 2012, Math 250

We study invariant subsets and invariant states of compact quantum group actions on unital C*-algebras. Concerning compact quantum group actions on commutative C*-algebras, we formulate the concept of compact quantum group orbits and prove some basic properties. Moreover, through analyzing invariant subsets and invariant states, we derive some interesting results about ergodic actions. Especially, we show that the unique invariant measure of a compact quantum homogeneous space with infinitely many points is non-atomic. As a result, countable compact metrizable spaces with infinitely many points are not quantum homogeneous spaces.

Nov 21

Fall Recess begins

Wednesday, November 21, 2012

Nov 26

Classes Resume

Monday, November 26, 2012

Nov 26

Algebra Seminar: Qi You (Columbia University)
Categorification of small quantum groups
3:00PM, Mon Nov 26 2012, Math 250

We propose an algebraic approach to categorify some small
quantum groups at prime roots of unity, using p-differential graded
algebras. If time permits, we will discuss the example of the sl(2) case.

Nov 27

Applied Mathematics Seminar: Rescheduled for Feb 26, 2013 (Sara Metcalf, UB)
4:00PM, Tue Nov 27 2012

Nov 28

Analysis Seminar: Peter Cho (Fields Institute)
Logarithmic derivatives of Artin L-functions at s=1
4:00PM, Wed Nov 28 2012, Math 250

Let K be a number field of degree n, and d_K be its discriminant. Then under the Artin conjecture, GRH and certain zero density hypothesis, we show that the upper and lower bound of the logarithmic derivative of Artin L-functions attached to K at s=1 are log log |d_K| and -(n-1) log log |d_K|, resp. Unconditionally we show that there are infinitely many number fields with the extreme logarithmic derivatives. They are families of number fields whose Galois closures have the Galois group as C_n, n=2,3,4,6, D_n, n=3,4,5, S_4 and A_5.

Dec 7

Last Day of Classes

Friday, December 7, 2012

Dec 10

Fall Semester Exams begin

Monday, December 10, 2012

Dec 17

Last Day of final exams

Monday, December 17, 2012

Dec 18

Winter Recess begins

Tuesday, December 18, 2012

Jan 21

Geometry/Topology Seminar
Mark Hagen (McGill University)
Contact graphs of CAT(0) cube complexes
4:00PM, Fri Jan 21 2011

Contact graphs of CAT(0) cube complexes

I will briefly define CAT(0) cube complexes and their contact graphs. The main theorem states that the contact graph of a cube complex is quasi-isometric to a tree. I will discuss this result using the example of regular tilings of the hyperbolic plane by squares, and give some applications to relative hyperbolicity and asymptotic finite dimensionality of groups acting on cube complexes, as well as to embeddings of cube complexes in products of trees.

Jan 28

Geometry/Topology Seminar
Sinem Onaran (University of Waterloo)
Knots in Contact Structures and Open Book Decompositions
4:00PM, Fri Jan 28 2011

Knots in Contact Structures and Open Book Decompositions

Due to Alexander, it is well known that every closed oriented 3-manifold has an open book decomposition. In this talk, we will define open book decompositions and discuss various examples. Further, we will discuss the importance of the open books in manifold theory, in particular in contact geometry. Then, we will focus on a class of knots in contact 3-manifolds called Legendrian knots. We will define a new invariant for Legendrian knots using open book decompositions. The invariant is called the support genus of a Legendrian knot. We will discuss the applications of this invariant and list several open problems related to the support genus of Legendrian knots.

Feb 10

Faculty Meeting
4:00PM, Thu Feb 10 2011, Math 250

Feb 17

Analysis Seminar
Guowei Zhao (UB)
Dipole-Dipole Correlation of sine-Gordon Model
4:00PM, Thu Feb 17 2011, Math 250

We consider the dipole-dipole correlation of the two-dimensional Coulomb gas/sine-Gordon model over β> 8π by renormalization group method. First we re-establish the renormalization group analysis for the partition function using nite range decomposition covariance. Then we extend the similar analysis to the correlation functions. Finally, we show a power-law decay over long-distance dipoles over Kosterlitz-Thouless phase.

Feb 23

Analysis Seminar
Jingbo Xia (UB)
4:00PM, Wed Feb 23 2011, Math 250

Feb 28

Applied Math Seminar
Quan Nguyen (UB)
Pulse dynamics in a multichannel optical waveguide
4:00PM, Mon Feb 28 2011, Math 250, University at Buffalo

We study the effects of Raman and weak cubic loss on the
dynamics of optical pulse parameters in a multichannel optical
waveguide. In the presence of Raman effects, we show that the dynamics
of pulse amplitudes in an N-channel transmission system is described by
an N-dimensional Lotka-Volterra model. We find the equilibrium states
with non-zero amplitudes and prove their stability by obtaining the
Lyapunov function. In the presence of weak cubic loss, we obtain the
analytic expressions for the amplitude and frequency shifts in a single
two-soliton collision and show that the impact of a fast three-soliton
collision is given by the sum of the two-soliton interactions.
Furthermore, we show that amplitude dynamics in an N-channel waveguide
system is described by a Lotka-Volterra model for N competing species.
These results uncover an interesting analogy between the dynamics of
energy exchange in pulse collisions and population dynamics in
Lotka-Volterra models. Joint work with Avner Peleg.

Mar 9

Analysis Seminar
Nhan-Phu Chung (UB)
4:00PM, Wed Mar 9 2011, Math 250

Mar 10

Colloquium
Yiqiang Li (Virginia Tech)
4:00PM, Thu Mar 10 2011

Mar 14

Colloquium
Boris Gershgorin (NYU)
4:00PM, Mon Mar 14 2011

Mar 18

Colloquium
Julien Paupert (U Fribourg)
4:00PM, Fri Mar 18 2011

Mar 24

Colloquium
David Hill (Stanford)
4:00PM, Thu Mar 24 2011, UB Math 250

Mar 25

Colloquium
Piotr Nowak (Texas A&M)
4:00PM, Fri Mar 25 2011, UB Math 250

Mar 31

Faculty Meeting
4:00PM, Thu Mar 31 2011, Math 250, University at Buffalo

Apr 5

Myhill Lectures
Benjamin Weiss (Hebrew University of Jerusalem)
Myhill Lectures
4:00PM, Tue Apr 5 2011, Math 250, University at Buffalo

Myhill Lectures

Apr 8

Geometry/Topology Seminar
Will Cavendish (Princeton University)
Finite sheeted covering spaces of 3-manifolds and the cohomology of solenoids
4:00PM, Fri Apr 8 2011, Math 122, University at Buffalo

Finite sheeted covering spaces of 3-manifolds and the cohomology of solenoids

In this talk I will discuss a cohomological approach to studying the finite sheeted covering spaces of a 3-manifold $M$. A well studied question in this setting is the following: given a $\pi_1$-injective immersion $f$ from a manifold $N$ into $M$, when can $f$ be lifted to a non-trivial finite sheeted covering space of $M$? I will describe how the inverse limit of the collection of all finite sheeted covering spaces of $M$, the universal solenoid over $M$, can be used to study this question. Topologically this solenoid is a Cantor set bundle $E\to M$, and recent work of Wilton-Zalesskii can be used to show, modulo the virtual fibered conjecture for hyperbolic 3-manifolds recently announced by Wise, that this bundle has trivial cohomology over finite coefficients groups for any compact 3-manifold $M$. I will then show how these results can be used to resolve Grothendieck's problem for the fundamental groups of many compact 3-manifolds, and how this in turn can be used as a tool to give a positive answer to the lifting problem stated above under suitable hypotheses.

Apr 12

Applied Mathematics / URGE Seminar
Michael Miksis (Northwestern University)
Moving Boundary Problems Associated with Biopreservation by Desiccation
4:00PM, Tue Apr 12 2011, Math 250, University at Buffalo

This talk will focus on several moving boundary problems associated with the preservation of cells by drying. Nature has provided us with a host of desiccation-tolerant organisms. Characteristic to each is the accumulation of internal sugars, e.g., trehalose, which are believed to play a major role in the success of the drying and rehydration process. When a sugar-water mixture dries, a glassy state is formed. Diffusion of water through this glassy region is anomalous and can be modeled by a fractional diffusion equation. The growth of the glassy region is central to the drying process. Analytical and numerical solutions of this moving boundary problem will be presented for several limiting cases. We will also formulate a hydrodynamic model of the drying process associate with a single cell. Limiting steady states and their stability will be discussed.

Prof. Miksis is a Fellow of the American Physical Society and Editor-in-Chief of the SIAM Journal on Applied Mathematics.
His visit is funded by URGE to Compute, the Math Department's undergraduate apprenticeship program in computational mathematics research. The common theme of this year's research projects is Continuum Modeling of Materials.

This talk will be comprehensible to undergraduates.

Apr 13

Analysis Seminar
Debashish Goswami (Indian Statistical Institute)
An overview of quantum isometry groups
4:00PM, Wed Apr 13 2011, Math 250, University at Buffalo

In this talk, I shall briefly describe the generalization of the concept of group of isometries of manifolds and metric spaces in the set-up of compact quantum groups and noncommutative geometry. In particular,for a noncommutative manifold given by spectral triple, satisfying certain natural regularity conditions, I shall discuss how to prove the existence of a universal object in the category of compact quantum groups which admit (co)-action on the underlying C* algebra commuting with the `Laplacian' of the spectral triple. This is the analogue of the group of Riemannian isometries. Similarly, an analogue of the group of orientation preserving Riemannian isometries will also be defined. Some concrete examples will be given to illustrate the theory.

Apr 15

Geometry/Topology Seminar
Jozef Prytycki (George Washington University)
4:00PM, Fri Apr 15 2011, 122 Math, University at Buffalo

Apr 18

Applied Math Seminar
Katie Liszewski (NCSU)
PDEs and $gl_{infty}$: an algebraic approach to an integrable problem
4:00PM, Mon Apr 18 2011, Math 250, University at Buffalo

PDEs and $gl_{infty}$: an algebraic approach to an integrable problem

Integrable equations, such as the KP equation from fluid mechanics, have many desirable properties. In particular, it is often easy to construct exact solutions of integrable PDEs.

Families of interesting exact solutions to the KP equation can be derived by studying the Lie algebra of ZxZ matrices. This technique gives a concise formulation of the KP hierarchy and an explicit description of N-solitons. Other integrable hierarchies, such as N-KP and Toda, can be studied just as easily with this method.

The charged free boson integrable hierarchy can be formulated using a slightly more general procedure. This hierarchy contains several PDEs that have potential as physical models. It is possible to compute soliton and Virasoro solutions for these PDEs. The charged free boson hierarchy also has several connections to KP; many of the solutions to the KP equation are solutions to a reduction of this hierarchy.

Apr 22

Geometry/Topology Seminar
Owen Baker (Cornell University)
4:00PM, Fri Apr 22 2011

Apr 25

Colloquium
Kimball Martin (University of Oklahoma)
Spectral geometry for Riemann surfaces
4:00PM, Mon Apr 25 2011

In his famous lecture, "Can one hear the shape of a drum?", Mark Kac asked if the harmonics of a Euclidean region determine its shape. While the answer is no in general, the harmonics determine much of the
geometry, and this is the basis of what is called spectral geometry. We will give a partial introduction to this subject, focusing on trace formulas, and discuss recent joint work with M. McKee and E. Wambach.

Apr 27

Analysis Seminar
Kai Wang (Fudan University)
4:00PM, Wed Apr 27 2011

Apr 28

Colloquium
Joel Bellaiche (Brandeis University)
Title : Extensions of Galois representations.
4:00PM, Thu Apr 28 2011, Math Building 250

Title : Extensions of Galois representations.

An impressing number of results and conjectures from various parts of number theory (to name two: Dirichlet's units theorem, and the conjecture of Birch and Swinnerton-Dyer) can be reformulated in terms of the existence or the non-existence of extensions of p-adic Galois representations (that is, extensions in the abelian category of the continuous finite-dimensional representation of the absolute Galois group of Q over an auxiliary p-adic field), and very general conjectures due to Beilinson and Bloch-Kato predict the dimension of the relevant spaces of extensions. In this talk,
I will try to explain and motivate those conjectures. I will then present an idea, basically due to Ribet and extended by many authors,
to construct interesting extensions of Galois representations, and present some recent results proved using that idea in the direction of the conjectures of Beilinson and Bloch-Kato.

Apr 30

New York Conference on Applied Mathematics
More information on the conference can be found on the conference web site at:
Saturday, April 30, 2011, Dept of Mathematics, University at Buffalo

More information on the conference can be found on the conference web site at:
http://gibbs.math.buffalo.edu/nycam/

May 2

Algebra Seminar
Craig Dodge (SUNY @ Buffalo)
Large dimension homomorphism spaces between Specht modules for
4:00PM, Mon May 2 2011, Math Building 250

Let F be a field of characteristic p. We show that HomFΣn (Sλ, Sμ) can have arbitrarily large dimension as n and p grow, where Sλ and Sμ are Specht modules for the symmetric group Σn. Similar results hold for the Weyl modules of the general linear group. Every previously computed example has been at most one-dimensional, with the exception of Specht modules over a field of characteristic two. The proof uses the work of Chuang and Tan, providing detailed information about the radical series of Weyl modules in Rouquier blocks.

May 9

Algebra Seminar
Craig Dodge (SUNY Buffalo)
Large dimension homomorphism spaces between Specht modules for symmetric groups, Part II
4:00PM, Mon May 9 2011, Math 122

Let F be a field of characteristic p. We show that HomFΣn (Sλ, Sμ) can have arbitrarily large dimension as n and p grow, where Sλ and Sμ are Specht modules for the symmetric group Σn. Similar results hold for the Weyl modules of the general linear group. Every previously computed example has been at most one-dimensional, with the exception of Specht modules over a field of characteristic two. The proof uses the work of Chuang and Tan, providing detailed information about the radical series of Weyl modules in Rouquier blocks.

Aug 29

Classes Begin
Monday, August 29, 2011

Sep 5

Labor Day Observed
Monday, September 5, 2011

Sep 6

Colloquium
Matt Fayers (Queen Mary
University of London)
Cores
4:00PM, Tue Sep 6 2011, 250 Math

This talk is on the combinatorics of partitions. If s is a positive integer, then an s-core is a particular type of partition which is important in representation theory. Given any partition which is not an s-core, there is a well-defined way to make it into an s-core by removing certain parts.

Now suppose t is another positive integer, coprime to s. Then a result of Anderson says that there are only finitely many partitions which are both s- and t-cores. Another result of Olsson says that if we start with an s-core and take its t-core, this is still an s-core.

We'll look at the question "when do two s-cores have the same t-core?". This turns out to be closely related to alcove geometry for Coxeter groups of type A. One result is a new proof of Olsson's result, and another is the result that of all the partitions which are both s- and t-cores, there is one which contains all the others.

Sep 12

Algebra Seminar
Yiqiang Li (University at Buffalo)
Three different geometric constructions of the irreducible representations of GL(n, C)
4:00PM, Mon Sep 12 2011, 250 Math

I'll present three different geometric constructions of the irreducible representation of $GL_n$ by line bundles on flag variety, homology (or constructable functions) on Springer fibers and intersection homology on affine Grassmannian. This is

based on Kamnitzer's lecture notes: Lectures on geometric constructions of the irreducible representations of GL_n on Arxiv:0912.0569.

Sep 16

Geometry/Topology Seminar
Jason Manning (University at Buffalo)
Recognizing 3-manifold groups
4:00PM, Fri Sep 16 2011, Math 250

I'll discuss the problem of recognizing presentations of
aspherical n-manifold groups, amongst general finite presentations.
Specifically, I'll describe joint work with Daniel Groves and Henry
Wilton on recognizing presentations of 3-manifold groups.

Sep 19

Algebra Seminar
Yiqiang Li (University at Buffalo)
Three different geometric constructions of the irreducible representations of GL(n, C), II.
4:00PM, Mon Sep 19 2011, Math 250

I'll present three different geometric constructions of the irreducible representation of $GL_n$ by line bundles on flag variety, homology (or constructible functions) on Springer fibers and intersection homology on affine Grassmannian. This is based on Kamnitzer's lecture notes: Lectures on geometric constructions of the irreducible representations of GL_n on Arxiv:0912.0569.

Sep 23

Geometry/Topology Seminar
Bernard Badzioch (University at Buffalo)
Title:
4:00PM, Fri Sep 23 2011, Math 250

Higher torsion invariants are invariants of bundles of smooth manifolds that can distinguish between bundles that are not diffeomorphic even if they are fiberwise homotopy equivalent. The talk will describe a construction of higher torsion by means of the secondary transfer of bundles. I will also explain how this approach to higher torsion provides an insight into some of its properties. This is a joint work with W. Dorabiala.

Sep 26

Algebra Seminar
Yiqiang Li (University at Buffalo)
Three different geometric constructions of the irreducible representations of GL(n, C), III.
4:00PM, Mon Sep 26 2011, Math 250

I'll present three different geometric constructions of the irreducible representation of $GL_n$ by line bundles on flag variety, homology (or constructible functions) on Springer fibers and intersection homology on affine Grassmannian. This is based on Kamnitzer's lecture notes: Lectures on geometric constructions of the irreducible representations of GL_n on Arxiv:0912.0569.

Sep 27

Colloquium
Judith Roitman (University of Kansas)
Paracompact box products
4:00PM, Tue Sep 27 2011, Math 150

The paracompact box products problem has been around for over
60 years, and while there are many partial results there is no truly
satisfactory resolution (yet). This talk will outline the problem and
and some recent work on it.

Sep 28

Rosh Hashanah (Classes cancelled after 6:00pm)
6:00PM, Wed Sep 28 2011

Sep 29

Rosh Hashana (Classes cancelled until 6:00pm)
Thursday, September 29, 2011

Oct 5

Analysis Seminar
Phu Chung (University at Buffalo)
NOTE: SPECIAL START TIME.
5:00PM, Wed Oct 5 2011, 250 Math

Sofi c groups were first introduced by Mikhail Gromov as a common generalizations
of amenable groups and residually finite groups. In 2008, in a remarkable break-
through, via modeling the dynamics of a measurable partition of probability space by
means of partitions of a finite space, Lewis Bowen showed how to defi ne entropy for
measure-preserving actions of countable so fic groups. Later, using ideas in operator
algebras, David Kerr and Hanfeng Li, developed a more general approach for both
measure and topological so fic entropies and established the variational principle for
this context.
In this talk, applying Kerr and Li's method, we will defi ne the topological pressure
for actions of so fic groups and establish the variational principle for topological
pressure. We also prove that the so fic topological pressure coincides with the classical
topological pressure when the acting group is amenable.

Oct 7

Yom Kippur (Classes cancelled after 6:00pm)
6:00PM, Fri Oct 7 2011

Oct 8

Yom Kippur (Classes cancelled until 6:00pm)
Saturday, October 8, 2011

Oct 12

Algebra Seminar
David Hemmer (University at Buffalo)
An introduction to the representation stability of Church and Farb.
4:00PM, Wed Oct 12 2011, Math 250

We will work through the recent paper “Representation theory and homological stability” by Thomas Church and Benson Farb.

Oct 14

Geometry/Topology Seminar
Jason Manning (University at Buffalo)
Survey of some recent work of Wise and collaborators
4:00PM, Fri Oct 14 2011, Math 250

Title: Survey of some recent work of Wise and collaborators

Oct 19

Algebra Seminar
David Hemmer (University at Buffalo)
An introduction to the representation stability of Church and Farb. (Part II)
4:00PM, Wed Oct 19 2011, Math 250

We will work through the recent paper “Representation theory and homological stability” by Thomas Church and Benson Farb.

Oct 21

Geometry/Topology Seminar
Xingru Zhang (Univeristy at Buffalo)
Exceptional Dehn fillings on hyperbolic knot manifolds
4:00PM, Fri Oct 21 2011, Math 250

In this talk, I'll give a brief survey of recent
progresses made on the study of exceptional Dehn fillings on
hyperbolic knot manifolds, including my joint work with
Steve Boyer and Cameron Gordon.

Oct 28

Geometry/Topology Seminar
Jason Manning (University at Buffalo)
Survey of some recent work of Wise and collaborators
4:00PM, Fri Oct 28 2011, 250 Math

In this talk I will give an overview of some exciting
recent work of Wise and his collaborators which was the topic of a
recent "http://comet.lehman.cuny.edu/behrstock/cbms/program.html"> CBMS
meeting at the CUNY Graduate Center. Among the results
announced by Wise: Every Haken hyperbolic 3-manifold is virtually
fibered. Every 1-relator group with torsion is residually finite.
These follow from deep new theorems about nonpositively
curved cube complexes.

Nov 2

Joint Analysis/Applied Math Seminar
Timur Akhunov (University of Calgary)
Title:
4:00PM, Wed Nov 2 2011, 250 Math

Title:
Local wellposedness of quasilinear systems of PDE generalizing KdV

ABSTRACT:
In this talk I will discuss local well-posedness of an initial value
problem associated to a system of PDE's generalizing the Korteweg-de
Vries Equation (KdV). These results, inspired by the approach of
Kenig-Ponce-Vega from the quasi-linear Schrödinger equation, apply to
a large class of systems of KdV type. I will give an outline of the
proof emphasizing the local smoothing estimates that allow the argument
to proceed via the artificial viscosity energy method.

Nov 4

Geometry/Topology Seminar
Robert Young (University of Toronto)
Higher-order filling functions in solvable groups
4:00PM, Fri Nov 4 2011, Math 250

Spaces with nonpositive curvature have many applications in geometric
group theory. For example, one application is the construction of
groups with unusual finiteness properties, like Stallings' group.
Similar constructions result in groups with unusual filling functions.
In this talk, we will describe how nonpositive curvature influences
the geometry of fillings in solvable groups and sketch some new
methods for bounding the Dehn function and higher-order Dehn functions
of subsets of nonpositively curved spaces.

Nov 9

Analysis Seminar
Jingbo Xia (University at Buffalo)
Essential normality of polynomial-generated submodules: Hardy space and beyond
4:00PM, Wed Nov 9 2011, Math 250

Click "more details" and see the attachment.

Nov 9

Algebra Seminar
David Hemmer (University at Buffalo)
An introduction to the representation stability of Church and Farb. (Part III)
4:00PM, Wed Nov 9 2011, Math 150

We will work through the recent paper “Representation theory and homological stability” by Thomas Church and Benson Farb.

Nov 11

Geometry/Topology Seminar
Ana Lecuona (Penn State)
Montesinos knots and the slice-ribbon conjecture
4:00PM, Fri Nov 11 2011, Math 122

The slice-ribbon conjecture states that a knot in the three sphere is
the boundary of an embedded disc in the four ball if and only if it
bounds a disc in the sphere which has only ribbon singularities. This
conjecture was proposed by Fox in the early 70s. There doesn't seem to
be any conceptual reason for it to be true, but large families of knots
(i.e. pretzel knots, two bridge knots) satisfy it. In this seminar we
will prove that the conjecture remains valid for a large family of
Montesinos knots. The proof is based on Donaldson's diagonalization
theorem for definite four manifolds.

Nov 16

Analysis Seminar
L.A. Coburn (University at Buffalo)
Berezin transform and Weyl-type unitary operators on the Bergman Space
4:00PM, Wed Nov 16 2011, Math 250

Click "more details" and see the attachment.

Nov 18

Geometry/Topology Seminar
Douglas LaFountain (Aarhus University)
Deligne-Mumford and the space of filtered screens
4:00PM, Fri Nov 18 2011, Math 122

For a genus g surface with s > 0 punctures and 2g+s>2,
decorated Teichmuller space (DTeich) is a trivial R_+^s-bundle over
the usual Teichmuller space, where the fiber corresponds to families
of horocycles peripheral to each puncture. As proved by R. Penner,
DTeich admits a mapping class group-invariant cell decomposition,
which then descends to a cell decomposition of Riemann's moduli space.
In this talk we introduce a new cellular bordification of DTeich
which is also MCG-invariant, namely the space of filtered screens.
After an appropriate quotient, we obtain a cell decomposition for a
new compactification of moduli space, which is shown to be homotopy
equivalent to the Deligne-Mumford compactification. This work is
joint with R. Penner.

Nov 23

Fall Recess
Wednesday, November 23, 2011

Nov 30

Applied Math Seminar
Debananda Chakraborty (University at Buffalo)
A gPC method for finding critical values of the sine-Gordon
4:00PM, Wed Nov 30 2011, 250 Math

We consider the sine-Gordon and nonlinear Schrodinger
equations with a point-like singular source term. The soliton interaction
with such a singular potential yields a critical solution behavior. That
is, for the given value of the potential strength or the soliton amplitude,
there exists a critical velocity of the initial soliton solution, around
which the solution is either trapped by or transmitted through the
potential. In this talk, we propose an efficient method for finding such
a critical velocity by using the generalized polynomial chaos (gPC)
method. For the proposed method, we assume that the soliton velocity
is a random variable and expand the solution in the random space
using the orthogonal polynomials. We consider the Legendre and
Hermite chaos with both the Galerkin and collocation formulations.
The proposed method finds the critical velocity accurately with spectral
convergence. Thus the computational complexity is much reduced. The
very core of the proposed method lies in using the mean solution instead
of reconstructing the solution. The mean solution converges exponentially
while the gPC reconstruction may fail to converge to the right solution due
to the Gibbs phenomenon in the random space. Numerical results confirm
the accuracy and spectral convergence of the method.

Dec 2

Geometry/Topology Seminar
Adam Sikora (University at Buffalo)
Character Varieties of surfaces as completely integrable systems
4:00PM, Fri Dec 2 2011, Math 122

It is known that the trace functions of a maximal set of
disjoint simple closed curves on a closed surface make its
SU(2)-character variety into an (almost) completely integrable
dynamical system. We prove an analogous statement for all rank 2 Lie
groups.We will discuss the possible generalizations of this result to
higher ranks.

Dec 8

Colloquium
Karen Vogtmann (Cornell)
Hairy graphs, automorphisms of free groups and modular forms
4:00PM, Thu Dec 8 2011, Math 250

Automorphisms of a free group can be studied
by considering their action on a space of finite graphs known as Outer space.
A classical theorem of Hurwicz implies that the homology of the
quotient of Outer space by the group of all (outer) automorphisms is
in fact an invariant of the
group Out(F_n).
A more recent beautiful insight of Kontsevich relates this homology to the Lie
algebra cohomology of a certain symplectic Lie algebra, and S. Morita used this
connection to find new homology classes for Out(F_n). In this talk I will
interpret Morita's classes in terms of finite graphs, and
then show how this graphical picture leads to the construction of large numbers
of new classes, including some which correspond to classical modular
forms for SL(2,Z).
(Joint work with Jim Conant and Martin Kassabov.)

Dec 9

Last Day of Classes
Friday, December 9, 2011

Dec 12

First Day of Final Exams
Monday, December 12, 2011

Dec 19

Last Day of Final Exams
Monday, December 19, 2011

Dec 20

Winter Recess Begins
Tuesday, December 20, 2011

Nov 3

Analysis Seminar
David Larson (Texas A&M University)
Operator-vlaued measures, dilations, and the theory of frames
4:00PM, Wed Nov 3 2010, Math 250, University at Buffalo

Operator-vlaued measures, dilations, and the theory of frames

We show that there are some natural associations between the theory of frames (including continuous frames and framings), the theory of operator-valued measures on sigma-algebras of sets, and the theory of normal linear mappings between von Neumann algebras. In this connection, frame theory itself is identified with the special case in which the domain algebra for the mapping is commutative. Some of the more important results and proofs for mappings in this case extend naturally to the case where the domain algebra is non-commutative. This happens frequently enough, and in profound enough ways, to justify defining a noncommutative frame to be an arbitrary ultraweakly continuous linear mapping between von Neumann algebras. It has been known for a long time that a sufficient condition for a unital bounded linear map between C*-algebras to have a Hilbert space dilation to a bounded homomorphism is that the mapping be completely bounded. Our theory shows that under suitable hypotheses even if it is not completely bounded it still has a Banach space dilation to a homomorphism, and the Banach space can be rather nice. We view this as a generalization of the known result that arbitrary framings have Banach dilations.

Nov 4

Colloquium
Adam Allan (University of Chicago)
Modular Centralizer Algebras Corresponding to p-Groups
4:00PM, Thu Nov 4 2010, Math 250, University at Buffalo

Modular Centralizer Algebras Corresponding to p-Groups

For P a finite p-group with subgroup Q and k a field of characteristic p, we consider the centralizer algebra kPQ consisting of elements in the group algebra kP that are invariant under the conjugation action of Q. In this talk, we will obtain a multiplicative decomposition of the algebra kPQ and use this to describe the Jacobson radical structure of kPQ. As further applications, we determine the representation type of kPQ and describe its cohomology with trivial coeffients.

Nov 10

Analysis Seminar
Yonatan Gutman (Universite Paris-Est Marne-la-Vallee)
Minimal Actions of Homeo(ω*) on Hyperspaces of ω
4:00PM, Wed Nov 10 2010, Math 250, University at Buffalo

Minimal Actions of Homeo(ω*) on Hyperspaces of ω

Let ω* = βω\ω, where βω denotes the Stone-Cech compactification of the natural numbers. This space, called the corona or the remainder of ω, has been extensively studied in the fields of set theory and topology. Following an earlier work of Glasner and Weiss we first identify the universal minimal dynamical system of the group G=Homeo(ω*) as the sub-system of “maximal chains” in the hyperspace Exp(Exp(ω*)). Here Exp(Z) stands for the hyperspace comprising the closed subsets of the compact space Z, equipped with the Vietoris topology. Using the dual Ramsey theorem and a detailed combinatorial analysis of what we call stable collections of subsets of a finite set, we obtain a complete list of the minimal sub-systems of the compact dynamical system (Exp(Exp(ω*)),G). The importance of this dynamical system stems from Uspenskij’s characterization of the universal ambit of G. These results apply as well to the Polish group Homeo(C), where C is the Cantor set. Joint work with Eli Glasner.

Nov 11

Collquium
Panayotis Kevrekidis (U Mass Amherst)
Dark Solitons and Vortices in Bose-Einstein Condensates: Oscillations and Precessions, Dynamics and Interactions in an Ultracold World
4:00PM, Thu Nov 11 2010, 250 Math, University at Buffalo

Dark Solitons and Vortices in Bose-Einstein Condensates: Oscillations and Precessions, Dynamics and Interactions in an Ultracold World

In this talk, we will present an overview of recent theoretical, numerical and experimental work concerning the static, stability, bifurcation and dynamic properties of coherent structures that can emerge in one- and higher-dimensional settings within Bose-Einstein condensates at the coldest temperatures in the universe (i.e., at the nanoKelvin scale). We will discuss how this ultracold quantum mechanical setting can be approximated at a mean-field level by a deterministic PDE of the nonlinear Schrodinger type and what the fundamental nonlinear waves of the latter are. Then, we will try to go to a further layer of simplified description via nonlinear ODEs encompassing the dynamics of the waves within the traps that confine them, and the interactions between them. Finally, we will attempt to compare the analytical and numerical implementation of these reduced descriptions to recent experimental results and speculate towards a number of interesting future directions within this field.

Nov 12

Colloquium
Alberto Apostolico (Georgia Institute of Technology and Universita di Padova)
Computing Surprise
4:00PM, Fri Nov 12 2010, Math 250, University at Buffalo

Computing Surprise

Classical information theory equates information to surprise. This talk examines the computational aspects of finding surprising regularities in sequences of diverse nature. The problem of modeling and detecting recurrent or rare patterns such as substrings or motifs and related associations or rules is pursued ubiquitously in order to compress data, unveil relationships, infer succinct descriptions, extract and classify features, etc. In molecular biology, special classes of patterns are variously implicated in facets of biological structure and function. And, in general, effective pattern discovery tools are becoming increasingly vital in the process of transforming data into insight and knowledge. This talk proposes a brief account of algorithmic pattern discovery and its applications, and highlights issues, products and challenges emerged in recent and current work.

Professor Apostolico’s visit is sponsored by URGE to Compute, the Math Department’s apprenticeship program in computational mathematics.

Nov 17

Analysis Seminar
Piotr Nowak (Texas A&M)
Exact Groups and Bounded Cohomology
4:00PM, Wed Nov 17 2010, Math 250, University at Buffalo

Exact Groups and Bounded Cohomology

Exactness is a very weak counterpart of amenability for groups. It is equivalent to Yu’s property A and to the existence of a topologically amenable action of the group on some compact space. Higson asked whether exactness admits a homological or cohomological characterization, similar to the ones amenable groups admit. In this talk we will give an answer to Higson’s question by characterizing exact groups via vanishing of bounded cohomology (or, equivalently, of the Hochschild cohomology of the convolution algebra). This provides a vast generalization of the classical result of B.E. Johnson, proved in the early 70's, for amenable groups.

Nov 30

Applied Math Seminar
Nate Barlow (UB)
The impulse response of a liquid sheet: An example of long-time algebraic growth
4:00PM, Tue Nov 30 2010, 250 Math, University at Buffalo

The impulse response of a liquid sheet: An example of long-time algebraic growth

Liquid sheet breakup is of interest in coating (e.g. glass and LCD manufacturing) and atomization (e.g. liquid propellant rocket engines). Research was undertaken to better understand the mechanisms that lead to breakup. In doing so, some fundamental concepts of stability have been brought into question.

Classical linear stability theory has the limitation of only being able to predict exponential growth. If the growth is non-exponential, the classical theory falsely interprets this a neutral stability. In this talk, series solutions will be shown that validate spatio-temporal stability predictions, revealing that long-term algebraic growth can arise from the accumulation of Fourier modes. This contrasts with exponential growth, which is usually paired with a specific mode.

In the talk, classical and spatio-temporal stability theories will be reviewed, with emphasis on the concepts of convective and absolute instability. Simple partial differential equations will be used to familiarize the audience with these ideas. The analysis will then be extended to liquid sheets. The particular configuration examined is a thin inviscid liquid sheet flowing in an ambient gas and subject to a localized perturbation.

For more details, see: N.S. Barlow, B.T. Helenbrook, and S.P. Lin. Transience to instability in a Liquid Sheet. J. Fluid Mech.; in press (2010). doi:10.1017/S0022112010004416. This talk will reflect on this paper, give further insight, and include animations!

Dec 1

Analysis Seminar
Keiko Dow (Canisius)
Extreme Points of Integral Families of Analytic Functions
4:00PM, Wed Dec 1 2010, Math 250, University at Buffalo

http://www.math.buffalo.edu/~hfli/Dow-abstract.pdf

Dec 8

Analysis Seminar
Xiaoqing Li (UB)
Canceled - to be rescheduled Spring semester.
4:00PM, Wed Dec 8 2010, 250 Mathematics Bldg, University at Buffalo

Canceled - to be rescheduled Spring semester.