Title: Degenerate, Generalized, and Reduced Whittaker models Abstract: Whittaker models are realizations of representations on a space of functions that transform in a certain way under the action of a unipotent group, and they have been central in both the local representation theory and the global theory of automorphic representations. For groups other than GL_n, […]
Title: Root Number Correlation Bias of Fourier Coefficients of Modular FormsAbstract:Â Â In a recent machine learning based study, He, Lee, Oliver, and Pozdnyakov observed a striking oscillating pattern in the average value of the P-th Frobenius trace of elliptic curves of prescribed rank and conductor in an interval range. Sutherland discovered that this bias extends to […]
Title: Rigid-analytic analogue of Artin-Grothendieck vanishing Abstract: The classical theorem of Andreotti and Frankel says that any Stein complex manifold has homotopy type of a CW complex of real dimension ≤ dimX. In particular, this implies that the cohomology groups H^i(X, A) vanish for any abelian group A and any i > dimX. This vanishing […]
Title: Igusa stacks and cohomology of Shimura varieties Abstract: Cohomology of Shimura varieties has drawn interest from number theory and representation theory. Following ideas developed by Caraiani-Scholze, Koshikawa, Santos, Hamann-Lee, I will explain how vanishing type of results for the generic part in the cohomology of Shimura varieties with torsion coefficients can be obtained, using […]
Title: Fourier Interpolation and the Weil Representation Abstract: In 2017, Radchenko-Viazovska proved a remarkable interpolation result for even Schwartz functions on the real line: such a function is entirely determined by its values and those of its Fourier transform at square roots of integers. We give a new proof of this result, exploiting the fact […]