3 may 2023 -- 09:15
[ONLINE] Università degli Studi di Milano-Bicocca
The speaker will deliver the talk online via Webex platform (see link below) and the meeting will be streamed also in room 3014, at the building U5-Ratio, Università degli Studi di Milano Bicocca.
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Meeting number (access code): 2741 809 0209
Meeting password: ZVbyAKn59D3 (98292565 from phones)
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 Szego kernel expansion. We then review some classical and recent developments for Toeplitz operators and their functional calculus. Finally, we study the spectral operator $\chi_k(T_P)$ constructed by the functional calculus of the first-order Toeplitz operator, which considers a set of eigenvalues in $k\,\mathrm{supp}\,\chi$ and weights them according to the values of a good cut-off function $\chi_k$ at each eigenvalue in the set. We will show that the kernel of the spectral operator $\chi_k(T_P)$ 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.