Events for 02/11/2016 from all calendars

Noncommutative Geometry Seminar

Time: 2:00PM - 3:00PM

Location: BLOC 220

Speaker: Yang Liu, Ohio State University

Title: Modular curvature for toric noncommutative manifolds

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. It 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 recovered the modular curvature functions found in the previous works. An important technical aspect of the computation is that it is free of computer assistance.

Graduate Student Organization Seminar

Time: 4:00PM - 5:00PM

Location: Blocker 506A

Speaker: Branimir Cacic, Texas A&M University

Title: Noncommutative tori I have known

Abstract: There is no escaping the noncommutative 2-torus, at least for the student of noncommutative geometry. It is certainly the most accessible nontrivial example of a noncommutative space, a generalised space whose coordinate algebra is no longer commutative, but it is also, perhaps, the most ubiquitous. In this talk, as time permits, I’ll give a brief, conceptual introduction to the noncommutative 2-torus in three of its many, many guises: generalised orbit space, quantised phase space, and hidden geometry of time-frequency analysis.