Hanukkah STAR mini-workshop 2025 

• Ilya Dumanski (MIT)

Perverse coherent sheaves on symplectic singularities

Abstract: Perverse constructible sheaves are ubiquitous in algebraic geometry and geometric representation theory. Bezrukavnikov introduced their coherent analog, called perverse coherent sheaves. For technical reasons, there are essentially two interesting examples when this notion is well-behaved: the nilpotent cone and the affine Grassmannian. In both these cases, this category is very meaningful and well-studied.

We will present a generalization of this construction to an arbitrary symplectic singularity. This may be seen as a step towards building the Kazhdan—Lusztig theory in this setting.

• Boris Feigin (HUJI)

Toroidal shifted algebras and extensions of vertex algebras

Abstract: Shifted affine algebras are the relatively new class of algebras which is extensively studied now. I plan to discuss the affinizations of such algebras .We get  the new class of algebras which has many applications. The interesting and important one - we can construct vertex algebras with big group of symmetries. Such algebras appear in geometric Langlands.

• Michael Finkelberg (HUJI)

Relative Langlands duality for osp(2n+1|2n)

Abstract: This is our joint work with A. Braverman, D. Kazhdan and R. Travkin. We prove that the S-dual of SO(2n+1) x Sp(2n) acting on the tensor product of their tautological representations U and V, is the symplectic mirabolic space V x T*Sp(2n) equipped with the action of two copies of Sp(2n). 

• Maria Gorelik (WIS)

TBA

• Victor Kac (MIT)

Modular invariant vertex operator algebras

Abstract: Vertex operator algebra (VOA) V with a Virasoro element L is called modular invariant if its normalized character ch_V (tau):=tr_V e^{2pi i tau (L_0 -c/24)} is a modular invariant function. The basic examples are rational VOA and affine VOA at admissible levels.

In my talk I will present a number of examples of modular invariant VOA beyond the rational ones, and state several conjectures and open problems about them. In conclusion I will discuss the quasi-invariant VOA, for which  the characters are quasi-modular functions. The examples include the simply-laced affine VOA  at negative integer level \geq -b, where b is the length of the longest leg in the affine Dynkin diagram.

• Vasily Krylov (Harvard)

TBA

• Shifra Reif (BIU)

TBA

• Vera Serganova (UC Berkeley)

TBA

• Ran Tessler (WIS)

Plabic tangles and Cluster structures in planar N=4 SYM amplitudes

Abstract: I will start by describing the nonnegative Grassmannian, the amplituhedron and their connection to the planar N=4 Super Yang Mills QFT. I will then describe cluster structures  that were discovered in amplitudes of this theory.

I will then explain the source of these phenomena, leading to the definition of plabic tangles and their operad structure.