Lectures "New Names in Math HSE-BIMSA". Speakers: Jianping Wang (BIMSA), Artem Prihodko (ILMS NRU HSE)
1) Higgs-de Rham flow for principal bundles and its applications. 2) Local coefficients for genuine equivariant cohomology
The zoom-session "New Names in Math HSE-BIMSA"
15th December 2025
Jianping Wang (BIMSA) 14:00-15:00 Moscow time
Higgs-de Rham flow for principal bundles and its applications
Abstract: In this talk, I will discuss the Higgs-de Rham flow for principal bundles. As applications, we show that semistability of principal bundles is preserved under change of structure groups, and that the Bogomolov inequality for principal bundles holds in positive characteristic. This is a joint work with Mao Sheng and Hao Sun.
Artem Prihodko (ILMS NRU HSE) 15:15:16:15 Moscow time
Local coefficients for genuine equivariant cohomology
Abstract: Genuine equivariant cohomology is an invariant of a topological space with an action of a compact Lie group finer than the naive Borel equivariant cohomology. Examples include equivariant topological K-theory, cobordisms and elliptic cohomology. In geometry instead of the usual singluar cohomology one is often more interested in its categorification - the category of sheaves on a topological space. In the talk I will describe a similar categorification for genuine equivariant cohomology.
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