Abstracts

Michael Finkelberg (Higher School of Economics)

Gaiotto conjectures for classical supergroups

This is a joint project with Roman Travkin and Alexander Braverman. We prove some conjectures proposed by Davide Gaiotto that include the Fundamental Local Equivalence of the geometric Langlands program and geometric Satake equivalence for some classical supergroups.

Yasmine Fittouhi (University of Haifa)

Title: Stratifications of the singular fibers of Mumford systems.

An integrable system is a dynamic system characterized by the existence of constants of motion and the existence of algebraic invariants, having a basis in geometry algebraic. In the 1970s, Mumford introduced a new completely integrable system defined on a smooth hyperelliptic curve. In the 2000s, Vanhaecke completed the description of the integrable Munford system by defining a Poisson structure on the phase space of the Mumford system.

In this talk I will present the Mumford system and study its singularities by determining when and why the Mumford system has singularities. For this we will use the concept of stratification. I will define two stratifications of the phase space M_g, one algebraic stratification and the other geometric stratification, and I will conclude this talk with the surprising results that arise from these stratifications.

Victor Kac (MIT)

Sunday, May 29:

Unitary representations of minimal W-algebras

Thursday, June 2:

Exceptional de Rham complexes

Ivan Motorin (Higher School of Economics, Ben Gurion University)

Resolution of singularities of the odd nilpotent cone of orthosymplectic Lie superalgebras

In this talk I will construct a Springer-type resolution of singularities of the odd nilpotent cone of the orthosymplectic Lie superalgebras osp(m|2n) for arbitrary m, n. If time allows, I will also talk about maximal orbits in the odd part of osp(m|2n) superalgebra under the natural action of SO(m) x Sp(2n) and their relation to the maximal adjoint orbits in so(m) and sp(2n) Lie algebras.

Vera Serganova (UC Berkeley)

On support varieties for algebraic supergroups

Alexander Sherman (Ben Gurion University)

Two spectral sequences for GL(1|1)-modules

Part of a project in progress, joint with I. Entova-Aizenbud and V. Serganova.

In this talk we will investigate a double complex defined on GL(1|1)-modules. This double complex has two spectral sequences associated to it, and each page of these spectral sequences, as well as their limits, give rise to rigid tensor functors. Further, the two spectral sequences are interchanged by contragredient duality. It turns out that the limits of these spectral sequences are close to semisimplification functors, and using this we may give explicit formulas for two semisimplification functors on GL(1|1)-modules, as well as their relationship to one another.

Using the above general consequences of spectral sequences, we obtain several results on properties of restrictions of simple modules to gl(1|1)-subalgebras for Kac-Moody and queer Lie superalgebras. This includes another proof of V. Serganova's recent result that the restriction of a simple GL(m|n)-module to a root subgroup GL(1|1) lies in the Karoubian tensor subcategory of GL(1|1) generated by irreducibles.

No knowledge of spectral sequences is required for this talk.

Ran Tessler (WIS)

Organizers: Maria Gorelia (Weizmann Institue of Science) and Alexander Sherman (BGU).

Contact: xandersherm [at] gmail [dot] com.