Tuesday, November 30, 2021
Time | Items |
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All day |
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4:00pm |
11/30/2021 - 4:15pm What does it mean to pick a ``random’’ hyperbolic surface, and how does one even go about ``picking’’ one? Mirzakhani gave an inductive answer to this question by gluing together smaller random surfaces along long curves; this is equivalent to studying the equidistribution of certain sets inside the moduli space of hyperbolic surfaces. In this talk I’ll describe a new method for building random hyperbolic surfaces by building random {\em flat} ones, and a template for translating theorems from the flat world to the hyperbolic one. As time permits, we will also discuss the application of this technique to Mirzakhani’s ``twist torus conjecture.’’ This is joint work (in progress) with James Farre. Location:
LOM 214
11/30/2021 - 4:30pm In 2003, Bump-Friedberg-Ginzburg constructed the generalized global theta representation on a metaplectic double cover of an odd special orthogonal group. which was used later to construct the non-minimal theta liftings between double covers of orthogonal groups. This can be viewed as a generalization of the classical theta correspondence. In particular, it enjoys the tower property similar to the Rallis tower in the classical setting. This raises the question of when the first non-zero lifting will occur for a fixed theta tower. Bump-Friedberg-Ginzburg analyzed this problem when the automorphic representations are generic. In this talk, we will show the way to construct such theta liftings and talk about some progress towards understanding the non-generic cases. Location:
Zoom
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