Tuesday, February 16, 2021
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All day |
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9am |
02/16/2021 - 9:00am Consider the function field $F$ of a smooth curve over $\mathbb{F}_q$, with $q \neq 2$. L-functions of automorphic representations of $\mathrm{GL}(2)$ over $F$ are important objects for studying the arithmetic properties of the field $F$. Unfortunately, they can be defined in two different ways: one by Godement--Jacquet, and one by Jacquet--Langlands. Classically, one shows that the resulting L-functions coincide using a complicated computation. Each of these L-functions is the GCD of a family of zeta integrals associated to test data. I will categorify the question, by showing that there is a correspondence between the two families of zeta integrals, instead of just their L-functions. The resulting comparison of test data will induce an exotic symmetric monoidal structure on the category of representations of $\mathrm{GL}(2)$. It turns out that an appropriate space of automorphic functions is a commutative algebra with respect to this symmetric monoidal structure. I will outline this construction, and show how it can be used to construct a category of automorphic representations. Location:
Zoom
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4pm |
02/16/2021 - 4:00pm We study properly convex real projective structures on closed 3-manifolds. A hyperbolic structure is one special example, and in some cases the hyperbolic structure may be deformed non-trivially as a convex projective structure. However, such deformations seem to be exceedingly rare. By contrast, we show that many closed hyperbolic manifolds admit a second convex projective structure not obtained through deformation. We find these examples through a theory of properly convex projective Dehn filling, generalizing Thurston’s picture of hyperbolic Dehn surgery space. Joint work with Sam Ballas, Gye-Seon Lee, and Ludovic Marquis. Location:
https://yale.zoom.us/j/96501374645
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