Events
The Department of Mathematics is pleased to host a variety of events throughout the year. For additional information about our seminars, lectures, colloquia, and related activities, please call (716) 645-6284 or contact us via general inquiry email: mathematics@buffalo.edu
Thank you for your interest in our events.
UPCOMING SEMINARS AND EVENTS
Mon, Mar 9, 2026
Algebra Seminar
Michaela Vancliff, University of Texas at Arlington
Generalizing classical Clifford algebras, graded Clifford algebras and their associated geometry
4:00 PM, 250 Mathematics Building
Graded Clifford algebras are non-commutative graded algebras related to classical Clifford algebras, and certain properties of such an algebra can be deduced from certain commutative geometric data associated to it. In particular, a standard result is that a graded Clifford algebra \(C\) is quadratic and Artin-Schelter regular with Hilbert series equal to that of a polynomial ring if and only if a certain quadric system associated to \(C\) is base-point free. About two decades ago, T. Cassidy and the speaker introduced a generalization of such an algebra, called a graded skew Clifford algebra, and they found that many results concerning graded Clifford algebra shave analogues in the case of graded skew Clifford algebras, provided the appropriate non-commutative geometric data is defined. More recently, T.Cassidy and the speaker defined a "skew" version of classical Clifford algebras, and related such algebras to graded skew Clifford algebras. Indeed,just as (classical) Clifford algebras are the Poincaré-Birkhoff-Witt (PBW) deformations of exterior algebras, skew Clifford algebras may be viewed as \(\mathbb{Z}_2\)-graded PBW deformations of quantum exterior algebras.
Fri, Mar 13, 2026
Topology and Geometry Seminar
Melissa Zhang (UC Davis)
Title: TBD
4:00 PM, 122 Mathematics Building
Fri, Apr 10, 2026
Applied Mathematics Seminar
Yulong Lu (U Minnesota)
Title: TBD
4:00 PM, Room: TBD
Fri, Apr 10, 2026
Topology and Geometry Seminar
Roberta Shapiro (University of Michigan)
TBA
4:00 PM, 122 Mathematics Building
TBA
Wed, Apr 15, 2026
Analysis Seminar
Rizwanur Khan, University of Texas at Dallas
TBA
4:00 PM, 250 Mathematics building
TBA
Mon, Apr 20, 2026
Algebra Seminar
Douglas Rizzolo, University of Delaware
TBA
4:00 PM, Mathematics Building
TBA
Thu, Apr 23, 2026
Colloquium
Brandis Whitfield (University of Wisconsin-Madison/SLMath)
Title: TBD
4:00 PM, 250 Mathematics Building
Fri, Apr 24, 2026
Topology and Geometry Seminar
Brandis Whitfield (University of Wisconsin-Madison/SLMath)
Title: TBD
4:00 PM, 122 Mathematics Building
Mon, Apr 27, 2026
Algebra Seminar
Michael Brannan, University of Waterloo
TBA
4:00 PM, Mathematics Building
TBA
Mon, May 4, 2026
Algebra Seminar
Xingting Wang, Louisiana State University
TBA
4:00 PM, Mathematics Building
TBA
Related Links
Myhill Lecture Series 2025
Seminars and Colloquia in the Past 12 Months
Fri, Feb 13, 2026
Applied Mathematics Seminar
Di Qi (Purdue University)
Reduced-order data assimilation models for predicting probability distributions of multiscale turbulent systems
4:00 PM, MATH 250
A new strategy is presented for the statistical forecasts of multiscale nonlinear systems involving non-Gaussian probability distributions. The capability of using reduced-order models to capture key statistical features is investigated. A closed stochastic-statistical modeling framework is proposed using a high-order statistical closure enabling accurate prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. A new efficient ensemble forecast algorithm is developed dealing with the nonlinear multiscale coupling mechanism as a characteristic feature in high-dimensional turbulent systems. To address challenges associated with closely coupled spatio-temporal scales in turbulent states and expensive large ensemble simulation for high-dimensional complex systems, we introduce efficient computational strategies using the random batch method. Effective nonlinear ensemble filters are developed based on the nonlinear coupling structures of the explicit stochastic and statistical equations, which satisfy an infinite-dimensional Kalman-Bucy filter with conditional Gaussian dynamics. It is demonstrated that crucial principal statistical quantities in the most important large scales can be captured efficiently with accuracy using the new reduced-order model in various dynamical regimes of the flow field with distinct statistical structures.
Wed, Feb 11, 2026
Analysis Seminar
Didier Lesesvre, Université de Lille
A connection between zeros and central values of \(L\)-functions
4:00 PM, Mathematics Building
\(L\) -functions appear as generating functions encapsulating information about various objects such as Galois representations, elliptic curves, arithmetic functions, modular forms, Mass forms, etc. Studying \(L\) -functions is therefore of utmost importance in number theory at large. Two of their attached data carry critical information: their zeros, which govern the distributional behavior of underlying objects; and their central values, which are related to invariants such as the class number of a field extension. We will discuss the important conjectures, one concerning the distribution of the zeros and one concerning the distribution of the central values, and explain a general principle that any restricted result towards the first conjecture can be refined to show that most corresponding central value shave the typical distribution predicted by the second conjecture. We will instantiate this general principle for a wide class of \(L\)- functions, and provide a more detailed discussion in the case of \(L\) -functions attached to modular forms.
Mon, Dec 8, 2025
Algebra Seminar
Mihai Fulger, University of Connecticut
Infinitesimal successive minima and convex geometry
4:00 PM, 250 Mathematics Building
We introduce infinitesimal successive minima of a line bundle at a point. We define them in terms of base loci and show that they are also the lengths of the largest simplex contained in the generic infinitesimal Newton-Okounkov body (iNObody) of the line bundle at the point. We characterize when the generic iNObody is simplicial. When the point is sufficiently general, we prove that the body is Borel-shaped, a property inspired by generic initial ideals. In particular, it satisfies simplicial lower bounds and polytopal upper bounds determined by its widths, which are again the infinitesimal successive minima. This is joint work with Victor Lozovanu
Mon, Dec 1, 2025
Algebra Seminar
Mahdi Asgari, Oklahoma State University and Cornell
Some dyadic Hecke algebras
4:00 PM, Mathematics Building
The Iwahori-Hecke algebras (in their various incarnations) are ubiquitous in the representation theory of both finite groups of Lie type, thanks to the works of Lusztig and others, and \(p\)-adic groups,following work of Howe-Moy and Bushnell-Kutzko among many others. In this talk I will focus on these objects in the often overlooked case of \(p=2\) and report on current joint work with Dan Barbasch. I hope to also explain our motivation for this study, which stems from studying certain interesting representations of non-linear cover groups.
Wed, Nov 19, 2025
Analysis Seminar
Alexandru Chirvasitu (UB)
Spectrum incompressibility and continuous commutativity preservers
4:00 PM, Mathematics Building
The Kaplansky-Aupetit question of whether Jordan epimorphisms between unital semisimple Banach algebras can be characterized as linear spectrum-shrinking surjections has spawned a vast literature on adjacent problems having to do with characterizing associative/Jordan morphisms as maps preserving various properties orinvariants. The talk’s central result is to the effect that continuous, commutativity-preserving, spectrum-shrinking maps from \(X\) to the \(n\times n\)matrices are either conjugations or transpose conjugations whenever \(n\ge 3\)and \(X\) is any one of: the general linear, special linear or unitary \(n\times n\) group, the set of semisimple matrices in either of the first two, or the set of \(n\times n\) normal matrices. Such maps in particular automatically preserve spectra, hence the title’s “incompressibility”. The proof leverages among other things the Fundamental Theorem of Projective Geometry, characterizing isomorphisms between lattices of subspaces as those induced by semi-linear isomorphisms.(joint with I. Gogić and M. Tomašević)
Fri, Nov 14, 2025
Applied Mathematics Seminar
Teng Wu (UB, School of Engineering and Applied Sciences)
AI-Empowered Wind and Hurricane Engineering
4:00 PM, MATH 250
Recent advancements in performance-based wind engineering have placed new demands on wind characterization (e.g., duration consideration), aerodynamics modeling (e.g., transient feature) and structural analysis (e.g., nonlinear response). While conventional approaches in computational and experimental wind engineering provide valuable tools to overcome many of these emerging challenges, noticeable increase in use of artificial intelligence (AI) suggests its great promise in facilitating the implementation of performance-based wind design methodology. This talk will discuss state-of-the-art machine learning tools (e.g., knowledge-enhanced deep learning and deep reinforcement learning) that are successfully applied to wind climate analysis, transient aerodynamics, nonlinear structural dynamics, shape optimization and vibration control. The final part of this talk will extend the application of AI tools to enhance the coastal city resilience under hurricane hazards (wind, rain, and surge).
Mon, Nov 10, 2025
Algebra Seminar
Stephen Landsittel, Hebrew University and Harvard
Analytic spread of binomial edge ideals
4:00 PM, 250 Mathematics Building
To an ideal \(J\) in a polynomial ring \(R\) over afield \(\mathbb{K}\) we associate its analytic spread \(\ell(J)\), the dimension of the fiber cone \(F(J)\) of \(J\). When \(J\) is graded and generated in a single degree \(d\), \(F(J)\) is a finite-type \(\mathbb{K}\)-algebra. To a graph \(G\) we associate its binomial edge ideal: \(J_G := \left(x_i y_j - x_jy_i\ :\ (i,j)\text{ is an edge of $G$}\right)\). We will discuss recent work where sharp bounds are given for \(\ell(J_G)\) and we compute the exact value when \(G\) is apseudo-forest. We accomplish this by computing the transcendence degree\(\mathrm{trdeg}_{\mathbb{K}} F(J)\) of the fiber cone over \(\mathbb{K}\).
Mon, Nov 3, 2025
Algebra Seminar
James Upton, UC Santa Cruz
Geometric Iwasawa theory via counting lattice points
4:00 PM, 250 Mathematics Building
Geometric Iwasawa theory studies the variation of class groups in \(\mathbb{Z}_p\)-towers of function fields. A new program initiated by Booher and Cais suggests replacing the role of the class group by (the p-divisible group of) the Jacobian. In this talk, we discuss the p-torsion part of the Jacobian, whose structure is described concretely in terms of certain numerical invariants called a-numbers. For suitably nice towers, we give a formula for the a-number as the number of lattice points in a region of the plane. A careful analysis of this region leads to an Iwasawa-style formula for these numbers. This is joint work with Joe Kramer-Miller, Jeremy Booher, and Bryden Cais.
Wed, Oct 29, 2025
Analysis Seminar
Byung-Jay Kahng (Canisius University)
Manageability of multiplicative partial isometries and quantum groupoids
4:15 PM, 250 Mathematics Department
Since the early attempts at generalizing the Pontryagin duality to the level of non-LCA groups and more recently locally compact quantum groups, the notion of a multiplicative unitary operator has been playing a central role, both in the theory and in constructing examples. In this talk, we will extend the notion to consider multiplicative partial isometries. The conditions include the pentagon equation, but more is needed. By also generalizing Woronowicz’s notion of manageability, it can be shown that the partial isometry determines a dual pair of C*-algebraic quantum groupoids of separable type. We will discuss how this is carried out, but also discuss the limitations of the framework, and possible ways to overcome them to achieve a full generalization.
Mon, Oct 27, 2025
Algebra Seminar
Nathan H. Fox, Canisius University
Mathematical models of genome rearrangement
4:00 PM, 250 Mathematics Building
In biology, a major driver of evolution is mutations in DNA structure. Given two organisms with similar but not identical genetic structure, biologists are interested in quantifying how “related” these organisms are. They are also interested in exploring what sequences of mutations might have led to these organisms. In this talk, I will give an overview of three mathematical models used to study genome rearrangement: the Single Cut or Join, Single Cut-and-Join, and Double Cut-and-Join models. Then,I will frame some of the biological questions in the language of these models and discuss some results. Then, time permitting, I will go into depth on some of the mathematical tools used to analyze these models.
Fri, Oct 24, 2025
Applied Mathematics Seminar
Julia Bernatska (U Connecticut)
Methods of algebraic geometry in application to completely integrable hierarchies
4:00 PM, Room 250
For many soliton-type equations, like the Korteweg-de-Vries (KdV), sine-Gordon, modified KdV, Boussinesq equations, etc. hierarchies of integrable hamiltonian systems were constructed. Each hamiltonian system possesses a spectral curve, and obtaining solutions is closely related to the uniformization problem for the curve. Solutions in terms of multiply periodic functions will be presented, along with a brief introduction to algebraic geometry and methods of constructing these solutions.
Wed, Oct 15, 2025
Analysis Seminar
Kehe Zhu (SUNY Albany)
The Bargmann transform and its applications
4:00 PM, Mathematics Building room 250
The Bargmann transform is an integral operatorthat maps \(L^2\) of the real line unitarily onto the Fock space \(F^2\) of thecomplex plane. Thus it establishes a correspondence between operators on \(L^2\)and those on \(F^2\), and serves as a bridge between real analysis, complexanalysis, harmonic analysis, and functional analysis. I will talk about theaction of the Bargmann transform on several classical operators on \(L^2\),including the Fourier transform, the Hilbert transform, and linear canonicaltransforms. These examples lead to several natural classes of operators on theFock space that were studied by various authors in the past few years,including my recent joint work with Xingtang Dong of Tianjin University inChina.
Fri, Sep 12, 2025
Algebra Seminar
Kay Rülling
Tame cohomology of the structure sheaf in mixed characteristic
4:00 PM, 250 Mathematics Department
This is joint work in progress with Alberto Merici and Shuji Saito. Let R be a complete discrete valuation ring of mixed characteristic with fraction field K. We show that the tame cohomology of Hübner-Schmidt on smooth K-schemes relative to R of(a twist of) the structure sheaf is ^1-invariant and is a finite R-module up to bounded torsion. This induces a canonical R-lattice in the cohomology of the structure sheaf of smooth proper K-schemes. Hence for example the eigenvalues of an automorphism of X acting on O-cohomolgy are integral over R. If X has a regular model over R and a mild version of resolutions of singularities in mixed characteristic holds, then this lattice would be the cohomology of this regular model. The interesting point is that weget the existence of such a lattice also in case X has no regular model and without using resolutions. To avoid resolutions in mixed characteristic we use classical results by Bartenwerfer and van der Put in rigid geometry.If time allows I can explain how we try to extend the above result to Hodge and de Rham cohomology.
Sun, Sep 7, 2025
Algebra Seminar
Mengwei Hu, Yale
On certain Lagrangian subvarieties in minimal resolutions of Kleinian singularities
Time: TBD, Mathematics Building
Kleinian singularities are quotients of \(\mathbb{C}^2\) by finite subgroups of \(SL_2(\mathbb{C})\). They are in bijection with the ADE Dynkin diagrams via the McKay correspondence. In this talk, I will introduce certain singular Lagrangian subvarieties in the minimal resolutions of Kleinian singularities that are related to the geometric classification of certain unipotent Harish-Chandra \((\mathfrak{g},K)\)-modules. The irreducible components of these singular Lagrangian subvarieties are \(\mathbb{P}^1\)s and \(\mathbb{A}^1\)s. I will describe how they intersect with each other through the realization of Kleinian singularities as Nakajima quiver varieties. Time permitting, we will also discuss the deformations of these singular Lagrangian subvarieties.
Mon, May 5, 2025
Algebra Seminar
Claudiu Raicu, University of Notre Dame
Polynomial functors and stable cohomology
4:00 PM, 250 Math Building
The theory of polynomial representations of the general linear group goes back to the thesis of Issai Schur at the turn of the 20th century. Such representations include the tensor, symmetric, and exterior powers of a vector space, and have been completely classified in the work of Schur when the underlying field is the complex numbers. While there has been significant progress since the work of Schur, the story over a field of positive characteristic remains largely unknown. In my talk I will describe some novel stabilization results for sheaf cohomology, and explain their connection to the study of polynomial representations / functors. This is based on joint work with Keller VandeBogert.
Fri, May 2, 2025
Applied Mathematics Seminar
Alex Bivolcic (UB), Applied Math Seminar, MATH250
Dispersive Shock Waves and Integrability of Modulation Equations for the Kadomtsev-Petviashvili Equation
3:00 PM, MATH250
Nonlinear wave phenomena comprise an important class of problems in mathematical physics. Remarkably, many of the governing equations, which arise as universal models in a variety of physical settings, are completely integrable infinite-dimensional Hamiltonian systems. Accordingly, such equations have a rich mathematical structure. This talk is concerned with the study of the Kadomtsev-Petviashvili (KP) equation, which comes in two variants, referred to respectively as the KPI and KPII equations. The KP equation is a universal model that describes the evolution of weakly dispersive, nonlinear wave trains in two spatial dimensions. It arises in many physical contexts, including shallow water waves, plasmas, acoustics, optics, and Bose-Eistain condensates. It is a completely integrable infinite-dimensional Hamiltonian system, and possesses an infinite number of conserved quantities. This talk is split into two parts: Part I: Two-Dimensional Reductions of the Whitham Modulation System for the KP Equation. Various two-dimensional reductions of the KP-Whitham system, namely the overdetermined Whitham modulation system for five dependent variables that describe the periodic solutions of the KP equation, are studied and characterized. Three different reductions are considered, corresponding to modulations that are independent of x, independent of y, and of t (i.e., stationary), respectively. Each of these reductions still describe dynamic, two-dimensional spatial configurations, since the modulated cnoidal wave generically has a nonzero speed and a nonzero slope in the xy plane. In all three of these reductions, the properties of the resulting systems of equations are studied. It is shown that the resulting reduced system is not integrable unless one enforces the compatibility of the system with all conservation of waves equations (or considers a reduction to the harmonic or soliton limit). In all cases, compatibility with conservation of waves yields a reduction in the number of dependent variables to two, three and four, respectively. As a by-product of the stationary case, the Whitham modulation system for the Boussinesq equation is also explicitly obtained. Par tII: Mach Reflection and Expansion of Two-Dimensional Dispersive Shock Waves Generated by Wedge-Type Initial Conditions. The oblique collisions and dynamical interference patterns of two-dimensional dispersive shock waves are studied numerically and analytically via the temporal dynamics induced by wedge-shaped initial conditions for the KPII equation. Various asymptotic wave patterns are identified, classified, and characterized in terms of the incidence angle and the amplitude of the initial step, which can give rise to either subcritical or supercritical configurations, including the generalization to dispersive shock waves of the Mach reflection and expansion of viscous shocks and line solitons. An eight-fold amplification of the amplitude of an obliquely incident flow on a wall at the critical angle is demonstrated. Applications of the results include bore interactions in geophysical fluid dynamics.
Tue, Apr 29, 2025
Algebra Seminar
Mee Seong Im, Johns Hopkins University
Automata, Boolean TQFT and pseudocharacters
4:00 PM, 250 Mathematics department
Finite-state automata (FSA) are important objects in theoretical computer science. I will describe how a Boolean-valued Topological Quantum Field Theory in dimension one carrying defects gives rise to an automaton. The regular language of the automaton appears through the evaluation of decorated one-manifolds. If time allows, I will explain how group characters and pseudocharacters appear in topological theory and TQFTs in one dimension with defects. Pseudocharacters are an essential tool in modern number theory. The former is joint with M. Khovanov, and the latter is joint with M.Khovanov and V. Ostrik.
Mon, Apr 28, 2025
Algebra Seminar
Padmini Veerapen, Tennessee Tech University
Regular algebras and their associated Manin universal quantum groups
4:00 PM, 250 Mathematics building
In this talk, we explore Artin-Schelter regular (henceforth, regular) algebras, noncommutative analogues of the polynomial ring. We examine some results pertaining to Manin universal quantum group of such a regular algebra. In particular, we analyze how a twist by an automorphism of an algebra may yield a 2-cocycle twist of the corresponding Manin universal quantum group. We exhibit this result in the context of the coordinate ring of the Jordan plane. Finally, we discuss a result relating Koszul regular algebras to their 2-cocycle twists using Raedschelders’ and Van den Bergh’s work on Manin’s universal quantum groups associated with Koszul regular algebras. This is joint work with H. Huang, V. C. Nguyen, K. B. Vashaw and X.Wang that was made possible by a SQuaRE at the American Institute of Mathematics.
Wed, Apr 23, 2025
Analysis Seminar
Xiaoqing Li, SUNY at Buffalo
Lower bounds of the Riemann zeta function on the line 1 and GL(3)
4:00 PM, 250 Math Building
In this talk, we will present a soft method deriving effective lower bounds for the Riemann zeta function on Re(s)=1, using the theory of GL(3) Eisenstein series.
Mon, Apr 21, 2025
Algebra Seminar
Michael R. Montgomery, Dartmouth College
Colored planar algebras and applications to Hadamard matrix quantum groups
4:00 PM, UB Mathematics building room 250
In this talk we define a colored planar algebra associated to a non-degenerate commuting square and identify the biunitary of the square as an element of the planar algebra. We use the biunitary to construct representations of annular algebras and quantum groups from the commuting square. When the corresponding quantum group is amenable we can compute elements in the spectrum of the adjacency matrix for a generating core presentation. This leads to two criteria which imply non-flatness of the biunitary and infinite dimension of the corresponding quantum group. Computations with these criteria are performed with a continuous family of biunitaries on the 3311 principal graph, Petrescu’s continuous family of complex Hadamard matrices, and type-II Paley Hadamard matrices. We conclude that all of Petrescu’s complex Hadamard matrices and all type-II Paley Hadamard matrices yield infinite-dimensional compact matrix quantum groups.
Fri, Apr 18, 2025
Applied Mathematics Seminar
Abner Salgado (University of Tennessee, Knoxville)
Energy, pointwise, and free boundary approximation of the obstacle problem for nonlocal operators
3:00 PM, Math 250
We consider the obstacle problem for a nonlocal elliptic operator, like the integral fractional Laplacian of order 0<s<1. We derive regularity results in weighted Sobolev spaces, where the weight is a power of the distance to the boundary. These are then used to obtain optimal error estimates in the energy norm. Next, we develop a monotone, two-scale discretization of the operator, and apply it to develop numerical schemes. We derive pointwise convergence rates for linear and obstacle problems governed by such operators. As applications of the monotonicity, we provide error estimates for free boundaries and a convergent numerical scheme for a concave fully nonlinear, nonlocal, problem. This presentation is based on several works in collaboration with: A. Bonito, J.P. Borthagaray, W. Lei, R.H. Nochetto, and C. Torres.
Wed, Apr 16, 2025
Analysis Seminar
Ryo Toyota, Texas A&M University
Expanders, geometric property (T), and warped cones
4:00 PM, 250 Math Building
Warped cones are metric spaces associated with dynamical systems, where their large-scale geometric properties reflect the dynamical properties of the underlying actions. In this talk, we discuss a large-scale invariant, called geometric property (T), for warped cones and show that if an action is ergodic, free, measure preserving and isometric on a Riemannian manifold, then the associated warped cone does not possess geometric property (T). This result negatively answers an open problem: whether the warped cone of an ergodic action by a group with property (T) possesses geometric property (T), and gives new examples of (super-)expanders without geometric property (T). This is based on a joint work with Jintao Deng.
Wed, Apr 9, 2025
Analysis Seminar
Hanfeng Li, SUNY at Buffalo
Local entropy theory, combinatorics, and local theory of Banach spaces
4:00 PM, 250 Math Building
In 1995 Glasner and Weiss showed that if a continuous action of a countably infinite amenable group on a compact metrizable space X has zero entropy, then so does the induced action on the space of Borel probability measures on X. I will discuss a strengthening of the Glasner-Weiss result, in the framework of local entropy theory, based on a new combinatorial lemma. I will also present an application of the combinatorial lemma to the local theory of Banach spaces. This is joint work with Kairan Liu.
Fri, Apr 4, 2025
Applied Mathematics Seminar
Tamas Horvath (applied math, Oakland U)
Space-Time Finite Element Methods - The Good, the Bad and the Ugly
3:00 PM, Math 250
Partial differential equations posed on moving domains arise in many applications such as air turbine modeling, flow past airplane wings, etc. The time-dependent nature of the flow domain poses an additional challenge when devising numerical methods for the discretization of such problems. One alternative when dealing with time-dependent domains is to pose the problem on a space-time domain and apply, for example, a finite element method in both space and time. These space-time methods can easily handle the time-dependent nature of the domain. In this talk, we present a space-time hybridizable discontinuous Galerkin method for the discretization of the incompressible Navier-Stokes equations on moving domains. This discretization is pointwise mass conserving and pressure robust, even on time-dependent domains. Moreover, high order can be achieved both in space and time. Numerical experiments will demonstrate the capabilities of the method.
Wed, Apr 2, 2025
Analysis Seminar
Yusheng Luo, Cornell University
Uniformization of gasket Julia set
4:00 PM, 250 Math Building
The quasiconformal uniformization problem for fractal sets is a classical question that has seen significant recent progress. In the 1970s, Ahlfors provided a geometric characterization of when a Jordan curve can be quasiconformally uniformized to a round circle. A closely related question–when a Sierpinski carpet can be quasiconformally mapped to a round carpet–has been extensively studied in both geometric and dynamical settings, with key contributions from McMullen, Bonk, and Bonk-Lyubich-Merenkov. In contrast, the problem of determining when a gasket can be quasiconformally mapped to a circle packing is more subtle. In this talk, I will discuss recent joint work with D.Ntalampekos that provides a characterization of when a gasket Julia set is quasiconformally equivalent to a circle packing. The proof builds on new results from some joint work with Y.Zhang on renormalization theory for circle packings.
Mon, Mar 31, 2025
Algebra Seminar
Jintao Deng, UB
Higher index theory for spaces with an FCE-by-FCEstructure
4:00 PM, Mathematics Building 250
The coarse Novikov conjecture claims that a certain assembly map from the K-homology of a metric space to the K-theory of its Roe algebra is injective. It has significant applications in geometry and topology of manifolds. Let \((1\to N_m\to G_m\to Q_m \to 1)_{m}\) be a sequence of extensions of finite groups. Assume that the coarse disjoint unions of\((N_m)_m\), \((G_m)_m\) and \((Q_m)_m\) have bounded geometry. The sequence\((G_m)_m\) is said to have an FCE-by-FCE structure, if the sequence \((N_m)_m\) and the sequence \((Q_m)_m\) admit fibered coarse embeddings into Hilbert spaces. In this talk, I will talk about the coarse Novikov conjecture for a space with an FCE-by-FCE structure. This is based a joint work with L. Guo, Q. Wang and G. Yu.
Mon, Mar 10, 2025
Algebra Seminar
Mohammad Javad Latifi Jebelli, Dartmouth College
Algebra of functions on a Hilbert space and QFT
4:00 PM, Mathematics Building room 250
We consider a space of square-integrable functions \(L^2(H)\) on an infinite-dimensional background space, a central mathematical notion in quantum field theory and stochastic processes. We then examine certain Banach algebras of functions within \(L^2(H)\) that are closed under pointwise multiplication. We describe the character spectrum of these algebras, followed by a discussion on induced CCR relations.
Fri, Mar 7, 2025
Topology and Geometry Seminar
Ali Guo (George Washington University)
From the Generalized Kauffman-Harary conjecture to incompressible surfaces.
4:00 PM, 122 Mathematics Building
For a reduced alternating diagram of a knot with a prime determinant p, the Kauffman-Harary conjecture states that every non-trivial Fox p-coloring of the knot assigns different colors to its arcs. This conjecture has been proved by Mattman and Solis in 2009. In 2022, we prove a generalization of the conjecture stated nineteen years ago by Asaeda, Przytycki, and Sikora: for every pair of distinct arcs in the reduced alternating diagram of a prime link with determinant d there exists a Fox d-coloring that distinguishes them. To explore the geometric approach of GKH, we also attempt to extend Mensaco’s meridian theorem to double branched cover of alternating prime non-split links by extending the "bubble construction".
Wed, Mar 5, 2025
Analysis Seminar
Ian Thompson, Universiry of Copenhagen
Residually finite-dimensional operator algebras: universal and co-universal representations
4:00 PM, 250 Math Building
Beginning in the 60s, Arveson wrote a massively influential series of papers on subalgebras of C*-algebras. A major thrust of these papers came from the fact that the choice of representations for a subalgebra plays a significant role in deciphering its structure. Quite recently, a major trend has been to understand which subalgebras admit a residually finite-dimensional representation, and to uncover their structural properties. In opposition to the C*-algebraic setting, residually finite-dimensional operator algebras have proven to form a much more flexible class of operator algebras. Here, we will discuss structural properties on the space of all residually finite-dimensional representations for a fixed operator algebra.
Mon, Mar 3, 2025
Algebra Seminar
Ian Thompson, University of Copenhagen
Noncommutative convex structures
4:00 PM, Mathematics Building room 250
The study of compact convex sets (in locally convex topological vector spaces) has a long history that has had deep connections with the foundations of functional analysis. For the purposes of operator theory, however, it is often necessary to consider new interpretations of convexity theory. The primary purpose of this talk is to discuss a new-found framework for noncommutative convex analysis, as well as showcase its applications to other disciplines.
Thu, Feb 27, 2025
Colloquium
Andrew Hirsch, Department of Computer Science and Engineering, UB
The Monadic Semantics of Effects or Making the Intensional Extensional
4:00 PM, Mathematics Building room 250
Programs act like mathematical functions. However, unlike mathematical functions, programs can also have impacts on the real world. This leads to a rejection of extensionality—i.e., the idea that two programs are equal if they always produce equal outputs given equal inputs. Instead, we must also pay attention to how they produce those outputs. This intensionality, however, makes it very difficult to reason about programs. One common trick, described in this talk, is to use ideas from category theory to capture the real-world impacts on programs in their output, allowing us to reason about programs as if they were mathematical functions.
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SPOTLIGHT: INTERDISCIPLINARY EVENT
UB Biological Sciences Seminar Series
MARCH 3, 2022; 228 NSC and via Zoom
Dr. Naoki Masuda, UB Mathematics, Gene network analysis: Revealing adaptive structural variants and quantifying omnigenic models.
Dec 3
Algebra Seminar- S. Paul Smith, University of Washington
Elliptic algebras
4:00PM, Mon Dec 3 2018, 150 Mathematics Bldg.
The algebras of the title form a flat family of (non-commutative!)
deformations of polynomial rings. They depend on a relatively prime
pair of integers n>k>0, an elliptic curve E, and a translation
automorphism of E. Quite a lot is known when n=3 and n=4 (and k=1),
in which case the algebras are deformations of the polynomial ring on
3 and 4 variables. These were discovered and have been closely studied
by Artin, Schelter, Tate, and Van den Bergh, and Sklyanin. They were
defined in full generality by Feigin and Odesskii around 1990 and
apart from their work at that time they have been little studied.
Their representation theory appears to be governed by, and best
understood in terms of, the geometry of embeddings of powers of E (and
related varieties like symmetric powers of E) in projective
spaces. Theta functions in several variables and mysterious identities
involving them provide a powerful technical tool.
This is a report on joint work with Alex Chirvasitu and Ryo Kanda.