Algebra seminar day, Wednesday May 14, 2025

9h00 – 9h45: Professor Efim Zelmanov (Shenzhen International Center for Mathematics, China)

Title: On Growth and Complexity functions.

Abstract: I will discuss history and recent results concerning (i) growth functions of groups, algebras, monoids and languages, (ii) complexity functions of infinite sequences.

10h00 – 10h45: Professor Jiping Zhang  (Peking University)

Title: Sylow  numbers of finite groups

Abstract: The Sylow theorem is the fundamental theorem of finite groups and  gives the existence and the number of maximal p-subgroups (  the  so-called Sylow p-numbers, or simply Sylow  numbers). The composition of  Sylow  numbers was analyzed by Marshall Hall .  At the end of the 20th century the question arised what influence Sylow numbers have on properties of the given finite group.  Also  it is proved recently that the integral group ring  ZG of a finite soluble group G determines its Sylow numbers.

11h00 – 11h45: Professor Vyacheslav Futorny (Shenzhen International Center for Mathematics, China)

Title: Representations of Lie algebras of vector fields on algebraic varieties

Abstract:  Lie algebras of vector fields on affine algebraic varieties is a rich source of simple infinite dimensional Lie algebras. We will discuss state of the art of their representation theory.