16:00
TBC
Please join us for reshments outside the lecture room from 1530.
Please join us for reshments outside the lecture room from 1530.
Conformal blocks appear in several areas of mathematical physics from random geometry to black hole physics. A probabilistic notion of conformal blocks using gaussian multiplicative chaos measures was recently formulated by Promit Ghosal, Guillaume Remy, Xin Sun, Yi Sun (arxiv:2003.03802). In this talk, I will show that the semiclassical limit of the probabilistic conformal blocks recovers a special case of the elliptic form of Painlevé VI equation, thereby proving a conjecture by Zamolodchikov. This talk is based on an upcoming paper with Promit Ghosal and Andrei Prokhorov.
This seminar will be at the normal time of 2pm, this is a change from previous announcements!
In the early 2010s, Riche and Williamson proposed new character formulas for simple and indecomposable tilting modules over reductive algebraic groups $G$ in positive characteristic. Even better, they showed their formulas would follow from a conceptually satisfying "categorical conjecture", which they were able to prove for $G = GL_n$. Our first goal in this talk will be to explain the statement of the categorical conjecture, indicating its connection to representation theory and assuming minimal background knowledge. Subsequently, we will introduce Smith–Treumann theory and outline how it may be applied to prove the categorical conjecture in general. Time permitting, we will conclude with remarks on future directions of study.
Abstract: The simplest solutions of integrable systems are special functions that have been known since the time of Newton, Gauss and Euler. These functions satisfy not only differential equations as functions of their independent variable but also difference equations as functions of their parameter(s). We show how the inverse scattering transform method, which was invented to solve the Korteweg-de Vries equation, can be extended to its discrete version.
S.Butler and N.Joshi, An inverse scattering transform for the lattice potential KdV equation, Inverse Problems 26 (2010) 115012 (28pp)