Gelfand-Fuchs cohomology for affine superspaces $A^{m,n}$
Organizers
Speaker
Time
Thursday, March 14, 2024 3:00 PM - 4:00 PM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
Let X be a smooth supermanifold of dimension (m, n) and V_X be the Lie superalgebra of super vector fields on $X$. The key ingredient in the computation of the Lie algebra cohomology groups $H*(V_X, k)$ is the local calculation in the formal neighborhood of a point. In the purely even case of dimension $(m, 0)$ this was done in the original work of Gelfand and Fuchs. Later several partial results were obtained by various people covering cases with $m \le n$.
I will present an outline of the calculation in the case of $m \ge n$, which fully settles the problem of local Gelfand-Fuchs cohomology for supermanifolds.
Speaker Intro
I have MSc degree in Applied Math / Computer Science from St. Petersburg IFMO and PhD in pure mathematics from Yale University. From 2014 to 2022 I held postdoctoral and visiting researcher positions in Japan, UK, Germany and France. I've joined BIMSA in 2023.
My current research interests include geometric representation theory, super groups and non-commutative algebraic geometry.