Francesco Sala

Francesco Sala (University of Western Ontario) приехал в Лабораторию алгебраической геометрии по приглашению научного сотрудника Лаборатории Михаила Финкельберга и заведующего Лабораторией Александра Кузнецова.

3 июня 2014 года в 14.00-15.20 Francesco Sala прочел доклад "Moduli spaces of sheaves on stacks, representation theory of affine Lie algebras and AGT conjecture".

Аннотация: In the present talk I describe some relations between moduli spaces of sheaves on stacks, representation theory of affine Lie algebras and AGT conjecture. In particular, I describe an orbifold compactification of the minimal resolution X_k of the A_k-1 toric singularities \C²/\Z_k inspired by the study of gauge theories on X_k. I introduce and characterize moduli spaces of (framed) sheaves over this orbifold. As an application, I show some relations between the equivariant cohomology of these moduli spaces, in the rank one case, and the representation theory of the affine Lie algebra of type \hat{A}_k-1. These relations imply AGT type relations for abelian quiver gauge theories on ALE spaces of type A_k-1.

3 июля 2014 года Francesco Sala выступил на семинаре "Геометрические структуры на многообразиях" с двумя докладами.

«Hilbert schemes of points on surfaces»
Abstract: In the present talk, I will introduce Hilbert schemes of points on smooth quasi-projective surfaces. I will describe in details Hilbert schemes of points on the complex affine plane. The talk will be very introductory and it will be based on the first Chapter of [Nakajima, Lectures on Hilbert schemes of points on surfaces].

«Hilbert schemes, moduli spaces of sheaves and gauge theories»
Abstract: Gauge theories in four dimension represent an important source of conjectures relating the (equivariant) cohomology and K-theory of Hilbert schemes of points on surfaces (or, more generally, of moduli spaces of framed sheaves) and representation theory of infinite-dimensional Lie algebras. The goal of the present talk is to give an overview of the main results and conjectures in this area.