Dixmier trace formulas and negative eigenvalues of Schroedinger operators on noncommutative tori

：Raphaël Ponge（四川大学）
：2022-01-07 15:30
：腾讯会议ID：105683543（无密码）

报告人：Raphaël Ponge（四川大学）

时  间：1月7日下午15:30

地  点：腾讯会议ID：105683543（无密码）

内容摘要:

In this talk, we shall first address a question raised by Alain Connes during a conference at Fudan University in Shanghai in 2017. We will also explain a link that have come to light only recently between noncommutative geometry and the work of Birman-Solomyak on semiclassical analysis of Schroedinger operators in the 70s. We will then present results obtained jointly with Ed McDonald (UNSW-Sydney) on Cwikel-type estimates on NC tori. As an application we obtain a version of Connes' integration formulas under very weak assumptions.  Further applications include version of the Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities for negative eigenvalues of Schroedinger operators on noncommutative tori. Ultimately, we get a seminclassical Weyl law for curved noncommutative tori, i.e., NC tori endowed with arbitrary Riemannian metrics.

个人简介：

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.

 

联系人：余世霖