Colloquium DATE 2019-10-03¡@16:10-17:00 PLACE ¼Æ¾ÇÀ]3174±Ð«Ç SPEAKER ªò°ê¼e °Æ±Ð±Â¡]¼sªF¤¤¤s¤j¾Ç¯]®ü®Õ°Ï¡^ TITLE G-Equivariant Szeg\H{o} Kernel Asymptotics on CR Manifolds ABSTRACT 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 Szeg\H{o} kernel is a complex Fourier integral operator, smoothing away from $\mu^{-1}(0)$, where $\mu$ denotes the CR moment map. By applying our result to the case when X also admits a transversal CR $S^1$ action, we deduce an asymptotic expansion for the $m$-th Fourier component of the G-equivariant Szeg\H{o} kernel as $m\to\infty$ 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.