Title: Why do cusp forms exist? Abstract: I will begin this talk by reviewing the Eichler-Shimura isomorphism between the space of cusp forms of weight k and level N, and a certain cohomology group. Shimura called this cohomology group as parabolic cohomology. In the context of automorphic forms on higher groups, such a cohomology group takes the form […]
Title: Stone duality between condensed mathematics and algebraic geometry Abstract: One classical incarnation of Stone duality is an anti-equivalence between the categories of profinite sets and Boolean algebras respectively. In this talk, we will discuss how this can be extended to a fully faithful embedding of condensed sets into fpqc sheaves over any base field. […]
Title: Integer Decomposition Property of lattice polytopes Abstract: Given a polytope (higher dimensional polygon) P and a non-negative integer k, we can multiply every point of P by k to obtain another polytope kP. One of the properties P can have is the integer decomposition property: if x is a point in kP, then there […]
Title: L^p bounds for spectral projectors on hyperbolic surfacesAbstract: In this talk I will present L^p boundedness results for spectral projectors on hyperbolic surfaces, focusing on the case where the spectral window has small width. I will show that the negative curvature assumption leads to improvements over the universal bounds of C. Sogge, thus illustrating […]
Title: Selmer groups, p-adic L-functions and Euler Systems: A new Framework Abstract: Selmer groups are key invariants attached to p-adic Galois representations. The Bloch—Kato conjecture predicts a precise relationship between the size of certain Selmer groups and the leading term of the L-function of the Galois representation under consideration. In particular, when the L-function does […]
Title: Singularity formation in incompressible fluids. Abstract: I will discuss a recent example of singularity formation in the 3d Euler equation. This is based on work joint with Federico Pasqualotto.
Title: TBA
Title: Bipartite Euler SystemsAbstract: I will give an example-based introduction to bipartite Euler Systems, starting with the construction in the case of Heegner points by Bertolini--Darmon from the early 2000's. I'll discuss the main obstacles in extending such methods to other settings, and survey some of the new constructions we have seen in the last […]
08:40 Breakfast in Krieger 413.09:10 Andreea Iorga (Chicago): Realising semi-direct products as Galois groups.09:55 Coffee break.10:15 Zeyu Liu (San Diego): A stacky approach to de Rham prismatic crystals over OK.11:10 Chengyang Bao (Chicago): Computing crystalline deformation rings via the Taylor-Wiles-Kisin patching method.12:00 Lunch […]
08:40 Breakfast in Krieger 413.09:10 Souparna Purohit (Penn): Distribution of the successive minima of the Petersson norm on cusp forms.09:55 Coffee break.10:15 Ruofan Jiang (Wisconsin): Mod p analogue of Mumford–Tate and André–Oort conjectures for GSpin Shimura varieties.11:10 Sun Woo Park (Wisconsin): On the prime Selmer […]
Title: Oscillatory integrals on manifolds and related Kakeya and Nikodym problems. Abstract: This talk is about oscillatory integrals on manifolds and their connections to Kakeya and Nikodym problems on manifolds. There are two types of manifolds that are particularly interesting: manifolds of constant sectional curvature and manifolds satisfying Sogge's chaotic curvature conditions. I will discuss these two […]
Title: Light condensed setsAbstract: This talk will introduce us to the light condensed setting, the new way of dealing with set-theoretic technicalities in the condensed setup. Particular emphasis will be on the changes, differences, and simplifications compared to the "old" approach, which we discussed last semester.