Physically inspired mathematics seminar at the Department of Mathematics at the University of North Carolina at Chapel Hill

The mathematics that appears in physics oftentimes has a characteristic internal structure, often captured by the word integrable. In many examples, this at first mysterious integrability structure was later connected with the representation theory of the corresponding algebraic objects: quantum groups, Virasoro algebras, or other infinite dimensiona Lie algebas. The study of these mathematical objects brings insights back into modern mathematical physics, as demonstrated in examples of conformal field theory and string theory. The goal of the seminar is to study this physically inspired mathematics.

Organizers: Lev Rozansky, Alexander Varchenko, Andrey Smirnov, and Slava Naprienko.

Guidance for Speakers: We strongly urge speakers to ensure that their presentations are lucid and accompanied by simple, illustrative examples that would be easy accessible by graduate students. We would appreciate if speakers dedicated at least half of their talk to the motivation behind their research, previous findings, and fundamental ideas.

The seminar is organized by the Department of Mathematics at the University of North Carolina at Chapel Hill.

The seminar meets at Phillips Hall, Room 385.

Date Speaker Title Abstract and Materials
3:00 pm, September 15 Slava Naprienko Integrable lattice models and symmetric functions, part 1 I will talk about how integrable lattice models from statistical mechanics unexpectedly became about the most powerful tool to study symmetric functions from representation theory and combinatorics of affine flag varieties. The talk will be accessible for graduate students and will feature multiple examples.
3:00 pm, September 22 Philip Tosteson Stability in the homology of the discriminant 1 hypersurface I will talk about the hypersurface in C^n defined by the equation $\prod_{i < j} (x_i - x_j) = 1$. This hypersurface has interesting symmetries, from the action of the alternating group permuting the variables and from the action of roots of unity by rescaling variables. I will describe how, as $n$ varies, these actions can be promoted to the action of a category that is closely related to the category of finite sets and injections. This category governs the behavior of the homology groups of these hypersurfaces for large values of $n$.
3:00 pm, September 29 Slava Naprienko Integrable lattice models and symmetric functions, part 2 I will talk about how integrable lattice models from statistical mechanics unexpectedly became about the most powerful tool to study symmetric functions from representation theory and combinatorics of affine flag varieties. The talk will be accessible for graduate students and will feature multiple examples.
3:00 pm, October 6 (Zoom) Masha Vlasenko TBA TBA
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4:00 pm, November 6 Hunter Dinkins TBA TBA
3:00 pm, November 10 Leonid Petrov TBA TBA
November 17 No meeting No meeting -- conflict with Workshop on Geometric Representation Theory and Moduli spaces