Geometry & Topology seminars - Wei-Chuan Shen

Mercoledì 3 maggio alle ore 09:15, per il ciclo di seminari "Geometry & Topology seminars at Unimib", Wei-Chuan Shen (University of Cologne) parlerà di

Title: Semiclassical spectral asymptotics of Toeplitz operators on CR manifolds

Abstract: This talk deals with semiclassical spectral asymptotics of Toeplitz operators on CR manifolds. First, we recall the notions of compact strictly pseudoconvex embeddable CR manifolds and Szegő kernel expansion. We then review some classical and recent developments for Toeplitz operators and their functional calculus. Finally, we study the spectral operator {\displaystyle \chi }k(TP) constructed by the functional calculus of the first-order Toeplitz operator, which considers a set of eigenvalues in k supp({\displaystyle \chi }) and weights them according to the values of a good cutoff function {\displaystyle \chi }k at each eigenvalue in the set. We will show that the kernel of the spectral operator {\displaystyle \chi }k(TP) is a semi-classical Fourier integral modulo a k-negligible smooth kernel. Time permitting, I will give some applications of such asymptotic expansion, which provides CR analogues (without group action assumption on our CR manifolds) of high power line bundle results in complex geometry.

Il seminario si svolgerà online tramite la piattaforma WebEx e sarà trasmesso in diretta streamoing in aula 3014 - edificio U5-Ratio.