Previous month Previous day Next day Next month
By Year By Month By Week Today Search Jump to month
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