Analysis Seminar
Title:Noncommutative Geometry and Semiclassical Analysis on Quantum Tori
Speaker:Raphaël Ponge （Sichuan University ）
Time: Wednesday, May 28, 2025, 14:30-16:00 (UTC+8)
Venue: Gewu Building, Room 315
Zoom ID: 976 1746 7912 (Password: 971230)
Link:https://zoom.us/j/97617467912?pwd=lzTsNI4eE3SYRaAzusNAxfQd3vabHf.1
Abstract: The semiclassical Weyl’s law is a landmark result in semiclassical analysis. In this lecture I will explain how it ultimately holds for a large class of quantum spaces. We will use this framework to solve a conjecture of E. McDonald and myself on semiclassical Weyl’s laws for curved quantum tori, i.e., quantum tori equipped with arbitrary Riemannian metrics. On the way we will see how to get spectral asymptotics for all negative order pseudodifferential operators on noncommutative tori. As a further application, we shall recover recent results of Sukochev-Xiong-Zanin on asymptotics for singular values of quantized derivatives on (flat) noncommutative tori. This bypasses the use of the C ∗ -algebra approach to the principal symbol used in the original article of Sukochev-Xiong-Zanin.
