Benjamin Hayes, Vanderbilt University
“Fuglede-Kadison determinants and sofic entropy”
I will discuss algebraic actions, which are actions of a countable, discrete group G by automorphisms of a compact, abelian, metrizable group X. Note this is a probability measure-preserving action, giving X the Haar probability measure. One is interested in classifying, or at least calculating invariants for, this class of probability measure-preserving actions. One common invariant to compute is the entropy of this action. I will discuss my results computing entropy for a large class of algebraic actions, when the group is sofic (the largest class of groups for which entropy is currently defined). The computation relates to operator algebraic invariants, namely the Fuglede-Kadison determinant, and operator algebraic techniques are important in the proofs.
MC 5501
Refreshments will be served in MC 5501 at 3:30 pm. Everyone is welcome to attend.