Noncommutative Geometry and Semiclassical Analysis on Quantum Tori
演讲者
Raphaël Ponge
时间
2025年07月02日 10:30 至 12:00
地点
A3-3-301
线上
Zoom 242 742 6089
(BIMSA)
摘要
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, which provides us with a quantum analogue of a well-known result of Birman-Solomyak from the 70s. If time is allowed it will be explained how these results to recent results of Sukochev-Xiong-Zanin on spectral asymptotics for quantized differentials on quantum tori.
演讲者介绍
Raphaël Ponge is a professor (distinguished researcher) at Sichuan University since 2019. His research interests include noncommutative geometry, global analysis, pseudodifferential operators, cyclic homology, and semiclassical analysis. He received his PhD from University of Paris-Saclay under the supervision of Prof. Alain Connes. Prior to moving to Sichuan University, he held faculty positions at Seoul National University, Tokyo University and University of Toronto. His research was published in various international journals including Advances in Mathematics, Communications in Mathematical Physics, Crelle's Journal, Journal of Functional Analysis, and Memoirs of the AMS. He received a 1,000 Talents award from Sichuan Province in 2020.