17 may 2023 -- 13:45
[ONLINE] Università degli Studi di Milano-Bicocca
The speaker will deliver the talk online via Webex platform (link below) and the meeting will be streamed also in room 3014, at the building U5-Ratio, Università degli Studi di Milano Bicocca.
Meeting number (access code): 2743 576 9398
Meeting password: aCdBmV6rV73 (22326867 from phones)
Abstract.
In complex geometry, Demailly and Bismut used the heat kernel asymptotics for Kodaira Laplacians to establish Morse inequalities on complex manifolds. It is natural to ask whether one can establish analogies to Morse inequalities on CR manifolds by studying the asymptotic behaviour of the heat kernel. In this talk, I will show how to establish the heat kernel asymptotics for Kohn Laplacian (particularly in the Heisenberg case) with values in high tensor power of line bundle. As an application, it provides a heat kernel proof of Morse inequalities on compact CR manifolds. This is a joint work with Chin-Yu Hsiao.