Monday, April 11, 2022
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All day |
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10am |
04/11/2022 - 10:30am Let $G=SL_d(R)$, $\Gamma=SL_d(Z)$ and $M$ be the subgroup of signs. I will talk about the counting and equidistribution of compact periodic orbits of the diagonal group on $\Gamma\backslash G/M$. Counting periodic diagonal orbits is a generalization of the prime geodesic theorem on compact hyperbolic surfaces, dating back to Huber, Margulis and Bowen. For $SL_2(Z)$ case, it is considered in Sarnak’s thesis. I will sketch a proof. We use Hopf coordinates, an idea of Roblin for hyperbolic cases, the angular distribution of lattices points and a version of non-escape of mass of periodic diagonal orbits. The talk is based on a recent joint work with Thi Dang. Location:
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4pm |
04/11/2022 - 4:30pm We define a class of transversal slices in spaces which are quasi-Poisson for the action of a complex semisimple group G. This is a multiplicative analogue of Whittaker reduction. One example is the multiplicative universal centralizer of G, which is equipped with the usual symplectic structure in this way. We construct a smooth partial compactification of Z by taking the closure of each centralizer fiber in the wonderful compactification of G. By realizing this partial compactification as a transversal in a larger quasi-Poisson variety, we show that it is smooth and log-symplectic. Location:
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