Онлайн лекции из серии научных презентаций исследований молодых ученых "Новые имена"

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.

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.