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AS-NCTS Seminar on Geometry and Several Complex Variables
11:00 - 12:00, October 4, 2019 (Friday)
R617, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 617室)
G-equivariant Szegő Kernel Asymptotics on CR Manifolds
Guokuan Shao (Sun Yat-Sen University)


Let X be a compact connected strongly pseudoconvex CR manifold. Assume that X admits a connected compact Lie group G action. Under certain natural assumptions on G, we show that the G-equivariant Szego kernel is a complex Fourier integral operator, smoothing away from μ−1(0), where μ denotes the CR moment map. By applying our result to the case when X also admits a transversal CR S1 action, we deduce an asymptotic expansion for the m-th Fourier component of the G-equivariant Szego kernel as m→∞ and compute the coefficients of the first two lower order terms. This talk is based on joint work with Chin-Yu Hsiao and Rung-Tzung Huang.


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