10:0011:00: 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 3fold flops. The connection is the noncommutative deformation theory of a crepant rational curve on a 3fold, which in turn exposes an ADE classification on noncommutative Jacobian algebras. This is joint work with Michael Wemyss (Glasgow).
11:3012:30: 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) onetoone correspondence with lattice polytopes of volume 4, and the latters admit a finite classification. In the narrow sense, I will talk about this xixcenturystyle 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.
l15:0016:00: 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 HardyLittlewood conjecture. This is based on joint works with Kaisa Matomäki, Maksym Radziwiłł, Xuancheng Shao and Terence Tao.
16:3017:30: 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 wellknown 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 boundedrank groups of Lie type (Helfgott; PyberSzabo; BreuillardGreenTao), but the conjecture is wide open for highrank 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. 
