Gelfand-Fuchs cohomology for affine superspaces $A^{m,n}$
演讲者
时间
2024年03月14日 15:00 至 16:00
地点
A6-101
线上
Zoom 638 227 8222
(BIMSA)
摘要
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.
演讲者介绍
Slava Pimenov于圣彼得堡IFMO取得应用数学/计算机科学硕士学位，在耶鲁大学取得纯数博士学位。2014年至2022年，他在日本、英国、德国和法国担任博士后和访问研究员，2023年加入BIMSA任助理研究员。他目前的研究兴趣包括几何表示理论、超群和非交换代数几何。