International Conference. S.O. Gorchinskiy – “Powers structures on Grothendieck rings of varieties”

Описание

International Conference, dedicated to the 75th birthday of Sabir M. Gusein-Zade
20.06.25

S. O. Gorchinskiy (Moscow, Russia)
Powers structures on Grothendieck rings of varieties

The talk is based on a work in progress with Danila Demin. In algebraic geometry the Grothendieck ring of varieties is being studied intensively, as well as its versions including the Grothendieck ring of varieties with actions of finite groups. There is a natural homomorphism between these rings and each of these rings has a natural lambda-structure defined in terms of (equivariant) symmetric powers of varieties. The homomorphism does not commute with lambda-structures. S.M. Gusein-Zade, I. Luengo, A. Melle-Hernandez introduced and studied the important notion of a power structure on a ring. Power structures are constructed from lambda-structures and different lambda-structures can lead to the same power structure. The main result is that the above homomorphism commutes with the power structures on the Grothendieck rings. This is obtained by means of a new general formula that expresses a power structure and the logarithm of a lambda-structure in terms of a combinatorics of trees.

General information
The conference will be held in the Faculty of Mathematics of the HSE University (Usacheva str. 6, Moscow).
Dates: 16 - 20 June 2025
Organizers: A. Buryak, V. Medvedev, A. Skripchenko

More information:
https://math.hse.ru/modern_aspects_singularity_theory25/
https://mccme.ru/ru/modern_aspects_singularity_theory2025/

Автор

Mathematics at HSE