报告时间：2023年11月17号下午3点-4点
报告地点：西南交通大学犀浦校区X30405
Speaker：Prof. Raphael Ponge（Sichuan University）
Title: Noncommutative geometry and semiclassical analysis
Abstract: Semiclassical analysis and noncommutative geometry are distinct fields within the wider area of quantum theory. Bridges between them have been emerging recently. This lays down on operator ideal techniques that are used in both fields. In this talk we shall present semiclassical Weyl’s laws for Schrödinger operators on noncommutative manifolds (i.e., spectral triples). This shows that well known semiclassical Weyl’s laws in the commutative setting ultimately holds in a purely noncommutative setting. This extends and simplifies previous work of McDonald-Sukochev-Zanin. In particular, this allows us to get semiclassical Weyl’s laws on noncommutative tori of any dimension $n\geq 2$, which were only accessible in dimension $n\geq 3$ by the MSZ approach. There are numerous other examples as well. The approach relies on spectral asymptotics for some weak Schatten class operators.
报告人简介：Raphael Ponge is a math professor in Sichuan University. His research interest is noncommutative geometry and index theory. The details can be found in his website https://raphaelponge.org/.
