Abstract: The moduli spaces of representations of Galois groups of p-adic fields with p-adic Hodge theoretic conditions play a pivotal role in the study of arithmetic properties of automorphic forms. Despite this, the geometry of these spaces is poorly understood, perhaps for good reason: conjecturally their complexity is bounded below by the modular representation theory of finite groups of Lie type. In this talk, I will survey some progress on the study of these moduli spaces in some special but important cases, where it turns out that they are closely related to degenerations of flag varieties into certain (deformed) affine Springer fibers. This is based on joint work with (various subsets of) D. Le, B. Levin and S. Morra.
Zoom link: https://yale.zoom.us/j/99305994163, contact the organizers (Gurbir Dhillon and Junliang Shen) for the passcode.