Semiclassical Analysis and Noncommutative Geometry
发布时间：2023年11月01日
浏览次数：1715
发布者: Wenqiong Li
主讲人： Raphael Ponge (Sichuan University)
活动时间： 从 2023-11-28 14:00 到 15:00
场地： 北京国际数学研究中心，全斋全29教室
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.
