Monday, March 14, 2022
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All day |
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4:00pm |
03/14/2022 - 4:00pm A limit point in the Furstenberg boundary of $G=SO^+(d,1)$ is called horospherical with respect to a discrete subgroup $\Gamma$ if every horoball based at the limit point intersects any $\Gamma$-orbit. Denote by $\Omega$ the non-wandering set in $T^1 \mathcal{M} = \Gamma \backslash T^1 \mathbb{H}^d$ with respect to the geodesic flow. A classical theorem of Dal’bo states that a horosphere in $T^1 \mathcal{M}$ is dense in $\Omega$ if and only if that horosphere is based at a horospherical limit point. In this talk I will present a higher-rank analogue of the above criterion for denseness of horospheres. Connection to the rank-one geometric proof will be emphasized. Joint with Hee Oh. Location:
LOM 206
03/14/2022 - 4:30pm Abstract: Let D be the sheaf of differential operators on a complex manifold M. If we turn on the Planck parameter, the ring D becomes a deformation quantization of the cotangent bundle of M. There is an analogue to this operation on the Betti side. Namely, we can "turn on the Planck parameter” for constructible sheaves. The resulting concept is called sheaf quantization. This concept (originally introduced by Tamarkin) has proven useful in many areas. In this talk, I will give an introduction to the concept, including applications to symplectic topology, WKB analysis, RH correspondence, etc. Location:
Zoom
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