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.
Title: A moduli-theoretic approach to heights on stacks.Abstract: A theory of heights of rational points on stacks was recently introduced by Ellenberg, Satriano and Zureick-Brown as a tool to unify and generalize various results and conjectures about counting problems over global fields. In this talk I will present a moduli theoretic approach to heights on stacks over […]
Title: Restricted Arithmetic Quantum Unique ErgodicityAbstract: The quantum unique ergodicity conjecture of Rudnick and Sarnak concerns the mass equidistribution in the large eigenvalue limit of Laplacian eigenfunctions on negatively curved manifolds. This conjecture has been resolved by Lindenstrauss when this manifold is the modular surface assuming these eigenfunctions are additionally Hecke eigenfunctions, namely Hecke-Maass cusp forms. I […]
Title: TBA
Title: Arithmetic Quantum Field Theory? Abstract: Mathematical structures suggested by quantum field theory have revolutionised important areas of algebraic geometry, differential geometry, as well as topology in the last three decades. This talk will introduce a few of the recent ideas for applying structures inspired by physics to arithmetic geometry.
Title: Maximal Subellipticity Abstract: The theory of elliptic PDE stands apart from many other areas of PDE because sharp results are known for very general linear and fully nonlinear elliptic PDE. Many of the classical techniques from harmonic analysis were first developed to prove these sharp results; and the study of elliptic PDE leans heavily on […]
Title: Solid modules Abstract: For this talk I would like to define and study solid abelian groups, whose construction is motivated in topology/analysis, by the desire to single out (metrizable) topological vector spaces that are complete.