Seminario Teoria de grupos

**Seminario teoría de grupos**

Andrei Jaikin

(UAM)

On the strong algebraic eigenvalue conjecture for sofic groups.

Jueves 8/2/2018

11:30, Aula 520, UAM

Abstract: Let $G$ be a countable group and let $K$ be a subfield of the field of complex numbers $CC$. Let $a$ be an element in the group algebra $K[G]$. Consider the associated operator $phi_a:l^2(G)to l^2(G)$ that acts as the right multiplication by $a$ (or, for the analysts, as the right convolution): $phi_a: vmapsto va$. We say that $lambdain CC$ is an eigenvalue of $a$ if there exists $0 e vin l^2(G)$ such that $phi_a(v)=lambda v$. If $G$ is finite, then it is clear that $lambda$ is algebraic over $K$. The strong algebraic eigenvalue conjecture claims that this holds for an arbitrary group $G$. This conjecture was formulated by Dodziuk, Linnell, Mathai, Schick, and Yates in 2003 in the case when $K$ is the field of algebraic numbers. In my talk I will explain the ideas of the proof of the conjecture for arbitrary $K$ when $G$ is a sofic group.

Location Jueves 8/2/2018 11:30, Aula 520, UAM