Geometry & Geometric Analysis Seminar
The Geometry and Geometric Analysis (GAGA) Seminar is an opportunity for geometers, topologists, and others from TCU and UT Arlington to learn about new topics of mutual interest. GAGA meets most weeks during the school year. You can find notes from past talks at the GAGA Note Repository, located in a secure off-campus location.
The next meeting of GAGA will be Thursday, September 12 from 4 to 5 pm in Tucker Technology (TUC) 243. Efton Park will speak on Traces, Determinants, and Toeplitz Operators. You can also attend via Zoom.
Abstract: I will start by discussing the general theory of traces and determinants for bounded operators on Hilbert space and show that in the case of Toeplitz operators on the circle, determinants of multiplicative commutators can be computed in terms of topological quantities. I will next discuss a general theory of traces and determinants on Banach algebras and apply that machinery to computing traces and determinants of Toeplitz-like operators associated to minimal flows on compact manifolds. I will not assume any specialized knowledge on any of these topics – I intend these talks to be like a stroll through a mathematical garden.