Résume | 11:30-12:30: Danylo Radchenko
Title: Polylogarithms and the Steinberg module
Abstract: I will talk about a surprising connection between the Steinberg module of rationals and a certain space of multiple polylogarithms on tori. I will expain how this idea leads to several important implications for Goncharov's program on structure of multiple polylogarithms, and if time permits I will also discuss how it relates to the Church-Putman-Farb conjecture for the cohomology of GL_n(Z). The talk is based on a joint work in progress with Steven Charlton and Daniil Rudenko.
14:45-15:45: Olga Trapeznikova
Title: Intersection cohomology of moduli spaces of semistable bundles on curves
Abstract: The study of the intersection cohomology of moduli spaces of semistable bundles on Riemann surfaces began in the 80’s with the works of Frances Kirwan. Motivated by the work of Mozgovoy and Reineke, in joint work with Camilla Felisetti and Andras Szenes, we give a complete description of these structures via a detailed analysis of the Decomposition Theorem applied to a certain map. We also give a new formula for the intersection Betti numbers of these moduli spaces, which has a clear geometric meaning. In this talk, I will describe our results.
16:05-17:05: Claire Burrin
Title: Rational points on spheres
Abstract: A sequence of point-sets is considered optimally distributed with respect to covering it its covering exponent is 1. I will discuss some new results on the covering exponent for sequences of rational points on spheres. This is joint work with Matthias Gröbner. |