The Local Langlands Program and Characteristic p
Explore the local Langlands program for GLn, focusing on representations in characteristic p and recent developments for GL2(K) in p-adic number theory.
Multivariable (φ, Γ)-Modules and Local-Global Compatibility
Explore multivariable $(\varphi, \Gamma)$-modules, extending Colmez's construction to $\mathrm{GL}_2(K)$ representations and comparing with Galois representations in mod $p$ cohomology of Shimura curves.
Towards a Mod p Langlands Correspondence for GL2
Explore the mod $p$ Langlands correspondence for $\mathrm{GL}_2(K)$, examining conjectures and recent progress in this open area of mathematical research.
Arithmetic Statistics and the Iwasawa Theory of Elliptic Curves
Explore arithmetic statistics and Iwasawa theory of elliptic curves, covering Selmer groups, Greenberg's Conjecture, and p-adic Birch and Swinnerton-Dyer Conjecture in this advanced number theory seminar.
Moduli Spaces of Local Systems in Algebraic Varieties
Delve into advanced mathematical concepts of local systems and Galois representations, exploring construction methods and parameter spaces in Betti, deRham, and l-adic settings.