Title：Modular geometry on noncommutative tori

Speaker：Yang Liu  (Max Planck Institute for Mathematics, Bonn)

Time：2019年7月12日       下午  16:00-17:30

Room：东区管理科研楼  0029cc金沙贵宾会1308室

Abstract：A general question behind the project is to explore the notion of intrinsic curvature for noncommutative spaces given in terms of Connes's spectral triple paradigm. It has only recent began (2014) to be understood on noncommutative two tori in the paper of Connes and Moscovici. The notion of curvature (or general local invariants) is modeled on spectral geometry of Riemannian manifolds. The new input, purely due to the quantum feature, is the modular theory of weights for Von Neumann algebras. In this talk, I will focus on some intriguing spectral functions arising from the interplay between the two components. I will present a bending phenomenon in contrast to the commutative world. My recent progress relates the calculus for those spectral functions to hypergeometric functions and cyclic homology/cohomology.