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. |
 |
10:00-11:00: Gavin Brown (University of Warwick)
Title: Noncommutative singularity theory
Abstract: I describe a noncommutative version of Arnold's classification of function germs and its application to the classification of simple 3-fold flops. The connection is the noncommutative deformation theory of a crepant rational curve on a 3-fold, which in turn exposes an ADE classification on noncommutative Jacobian algebras. This is joint work with Michael Wemyss (Glasgow).
11:30-12:30: Alexander Esterov (LIMS)
Title: Solvable systems of equations, Galois groups in enumerative geometry, and small lattice polytopes
Abstract: The general polynomial of a degree higher than 4 cannot be solved by radicals. This classical theorem has a multidimensional version: solvable general systems of polynomial equations are in (almost) one-to-one correspondence with lattice polytopes of volume 4, and the latters admit a finite classification. In the narrow sense, I will talk about this xix-century-style result. In a broader sense, we shall look at the Galois groups of problems of enumerative geometry (such as Schubert calculus), and how their study leads to seemingly distant topics such as polyhedral geometry and braid groups.
l15:00-16:00: Joni Teräväinen (University of Turku)
Title: Uniformity of the primes in short intervals
Abstract: Gowers norms are a measure of the pseudorandomness properties of a set. Green, Tao and Ziegler showed in 2012 that the set of prime numbers is Gowers uniform, in the sense that a suitably normalised version of it has small Gowers norms. We show that the primes are Gowers uniform also when restricted to short intervals [x,x+x^c] for suitable c. Morover, the admissible value of c is smaller if we look at primes in almost all short intervals. I will also discuss an application of such results to an averaged version of the Hardy--Littlewood conjecture. This is based on joint works with Kaisa Matomäki, Maksym Radziwiłł, Xuancheng Shao and Terence Tao.
16:30-17:30: Sean Eberhard (Queen's University)
Title: Diameter bounds for finite classical groups generated by transvections
Abstract: The diameter of a group G with respect to a symmetric generating set X is the smallest integer d such that every element of G is the product of at most d elements of X. A well-known conjecture of Babai predicts that every nonabelian finite simple group G has diameter (log |G|)^O(1) with respect to any generating set. This is known to be true for bounded-rank groups of Lie type (Helfgott; Pyber--Szabo; Breuillard--Green--Tao), but the conjecture is wide open for high-rank groups. There has bee a good deal of progress recently for generating sets containing either special elements or random elements. In this talk I will outline the proof that the conjecture holds for the classical groups SL_n(q), Sp_{2n}(q), SU_n(q) and any generating set containing a transvection. The proof is based essentially on (a) the positive resolution of Babai's conjecture in bounded rank and (b) a result of Kantor classifying finite irreducible linear groups generated by transvections. |
|
