报告题目：Noncommutative geometry and semiclassical analysis
报告时间：2023年11月17号下午3点-4点
报告地点：金沙威尼斯欢乐娱人城犀浦校区X30405
报告人：Prof. Raphael Ponge（Sichuan University）
摘要：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：Prof. Ponge is professor (senior researcher) at Sichuan University in Chengdu since 2019. He is an expert on noncommutative geometry, but his research also involves pseuudodifferential operators, differential geometry, homological algebra, and spectral theory. He did his PhD at University Paris-Saclay (formerly known as University Paris-Sud) in Orsay (France) under the supervision of Prof. Alain Connes. Before moving to Sichuan University, he held academic positions in Korea, Japan, Canada and USA.
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