By Year By Month By Week Today Search Jump to month January February March April May June July August September October November December 2018 2019 2020 2021 2022 2023 2024 2025
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