PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Nigel Higson, Stephanie Zerby, John Roe.

Title:Modular curvature for toric noncommutative manifolds
Seminar:Noncommutative Geometry Seminar
Speaker:Yang Liu, Ohio State University
Abstract:
A general question behind the talk is to explore a good notion for intrinsic curvature in the framework of noncommutative geometry started by Alain Connes in the 80’s. This has only recently begun (2014) to be comprehended via the intensive study of modular geometry on the noncommutative two tori. In this talk, we extend recent results on the modular geometry on noncommutative two tori to a larger class of noncommutative manifolds: toric noncommutative manifolds. The first contribution of my work is a pseudo differential calculus which is suitable for spectral geometry on toric noncommutative manifolds. As a main application, we derive a general expression for the modular curvature with respect to a conformal change of metric on toric noncommutative manifolds. By specializing our results to the noncommutative two and four tori, we recover the modular curvature functions found in previous works. An important technical aspect of the computation is that it is free of computer assistance.

Room Reservation Information

Room Number:MB106
Date:04 / 28 / 2016
Time:02:30pm - 03:30pm