Mikhail Khovanov (Johns Hopkins University)

April 30, May 1 & 2, 2025: Join us for for the Myhill Lecture Series featuring Mikhail Khovanov (Johns Hopkins University). The series, Link homology and other applications of defect networks, includes talks on: Topological quantum field theories in classical computation and in graph theory; Diagrammatics of categorified quantum groups; and, Link homology from foams.

April 30, Wednesday, 4:00 P.M.
Location TBA
Lecture 1: Topological quantum field theories in classical computation and in graph theory
Abstract: The relation between TQFTs (topological quantum field theories) and quantum computation is well-known. We will explain a relation between one-dimensional TQFTs with defects and finite state automata and a relation between two-dimensional TQFTs and graph theory, including graph homomorphisms and perfect matchings.

May 1, Thursday, 4:00 P.M.
250 Mathematics Building
Lecture 2: Diagrammatics of categorified quantum groups
Abstract: How to take the divided power of a functor? We explain the construction, based on nilHecke algebras, and its extension to categorification of quantum groups.

May 2, Friday, 4:00 P.M.
250 Mathematics Building
Lecture 3: Link homology from foams
Abstract: A perfect model for link homology is a functor from the category of link cobordisms to the category of vector spaces or abelian groups. The talk will review the construction of such a functor based on Robert-Wagner foam evaluation.

Bio: Mikhail Khovanov is a Russian-American professor of mathematics who works on representation theory, knot theory, and algebraic topology. He is known for introducing Khovanov homology for links, which was one of the first examples of categorification. Khovanov earned a PhD in mathematics from Yale University in 1997, where he studied under Igor Frenkel.
Research Interests: Categorification, representation theory, low-dimensional topology

Wikipedia:  In 2000 Mikhail Khovanov constructed a certain chain complex for knots and links and showed that the homology induced from it is a knot invariant (see Khovanov homology). The Jones polynomial is described as the Euler characteristic for this homology.