Pseudo-differential approach to heat asymptotic on noncommutative two tori

Speaker: 

Yang Liu

Affiliation: 

The Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste

Date: 

Wed, 18/09/2019 - 12:00pm

Venue: 

RC-4082, The Red Centre, UNSW

Abstract: 

Modeled on spectral geometry of Riemannian manifolds, the asymptotic expansion of the heat operator of a geometric elliptic operator provides a functional analytic approach to detect  local invariants, especially, the notion of  intrinsic curvature, of  noncommutative manifolds. In this talk, I will focus on some explicit elliptic operator on noncommutative two tori to illustrate  the algorithm, based on symbol calculus of pseudo-differential operators, of computing the heat coefficients and discuss  some intriguing structure of the coefficients that still begging for more conceptual interpretation.

School Seminar Series: