Title: p-adic L-functions for GSp(4)times GL(2) Abstract: I'll explain a construction of p-adic L-functions for GSp(4)times GL(2) by using Furusawa's integral and the proof of its interpolation formula. I'll describe how local functional equations are used to compute the zeta intgerals at p and how the archimedean integrals are computed by using Yoshida lifts together […]
Title and abstract TBA
Title: The Weil representation.
Topic: Formalizing ∞-Category Theory in Lean
Title: The Saint Venant inequality and quantitative resolvent estimates for the Dirichlet Laplacian.Abstract: Among all cylindrical beams of a given material, those with circular cross sections are the most resistant to twisting forces. The general dimensional analogue of this fact is the Saint Venant inequality, which says that balls have the largest “torsional rigidity” among […]
Title: Reconstructing schemes from their étale topoi.Abstract: In Grothendieck’s 1983 letter to Faltings that initiated the study of anabelian geometry, he conjectured that a large class of schemes can be reconstructed from their étale topoi. In this talk, I’ll discuss joint work with Magnus Carlson and Sebastian Wolf that proves Grothendieck’s conjecture for infinite fields. Specifically, we […]
Title: Towards Bezrukavnikov's geometrization of affine Hecke algebras in mixed-characteristics Abstract: Let G be a connected reductive group over a p-adic field. Kazhdan and Lusztig established an isomorphism between the extended affine Hecke algebra of G and certain equivariant K-group of the Steinberg variety of the Langlands dual group of G. This isomorphism plays a crucial […]
Title and abstract TBA
Title: Transfer operators for the relative trace formula. (Cont.) Abstract: Last time I presented an explicit formula for transfer operators that relate test measures and characters between the double quotients HG/H, for any rank-one homogeneous space G/H and the Whittaker model of SL(2) or PGL(2). In this talk, I will give a possible explanation for […]
Title: Restriction estimates for spectral projectionsAbstract: Restriction estimates for spectral projections have been widely studied since the work of Burq, Gérard, and Tzvetkov as a method for investigating eigenfunction concentration. The problem of establishing the optimal $L^p$ bounds for the restriction of Laplace-Beltrami eigenfunctions remains open, particularly when the restriction submanifold is of codimension 1 […]
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