Mikhail Gorsky (Univ. Vienna): Hall algebras and functions on categories
Abstract: Degenerations of quantized enveloping algebras can be studied via quantum degree cones. In my work with Xin Fang, we interpreted such cones from the perspective of relative homological algebra and functor categories. In this setting, degenerations of quantized enveloping algebras and more general Hall algebras are induced by certain functions on objects in exact categories, which we call valuations, which give points in quantum degree cones. Chuang and Lazarev recently introduced another class of functions on objects in categories: rank functions on triangulated categories, generalizing, in particular, Sylvester rank functions and mass functions of Bridgeland stability conditions. In my talk, I will present some parts of my recent work with Teresa Conde, Frederik Marks, and Alexandra Zvonareva on the functorial approach to rank functions and will try to explain a connection between these frameworks. If time permits, I will explain potential applications of these methods to (quantum) cluster algebras.
The Algebra Seminar was founded by Vladimir Korinek in the early 1950's and continued by Karel Drbohlav until 1981. The seminar resumed its activities in 1990 under the guidance of Jaroslav Jezek and Tomas Kepka. Since 1994, the seminar is headed by Jan Trlifaj.
Presently, the seminar is supported by GACR. It serves primarily as a platform for presentation of recent research of the visitors to the Department of Algebra as well as members of the Department and their students.