September 10, 2015
4:30 pm
-
5:30 pm
Cockins Hall 240
Title: Determinants in K-theory and operator algebras
Speaker: Joseph Migler (OSU)
Abstract: Given two invertible matrices, their multiplicative commutator, A B A^{-1} B^{-1}, is has determinant 1. The notion of determinant can be extended to infinite dimensions, but this result no longer holds. Remarkably, it turns out that this is related to K-theory, which is an analogue for rings of algebraic topology. This talk will present these ideas and some recent index-type theorems for calculating these determinants. We will see a number of examples and, time permitting, applications to constant-diagonal matrices and their infinite dimensional versions. This talk will assume no prior experience with K-theory or functional analysis.
