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Explore advanced topics in arithmetic geometry through this comprehensive seminar series featuring 25 specialized lectures from leading researchers at the Institute for Advanced Study and Princeton. Delve into cutting-edge research areas including p-adic geometry, Hodge theory, modular forms, and algebraic topology through presentations on integrality of Betti moduli spaces, Riemann-Hilbert correspondence in nonarchimedean geometry, and stacky perspectives on p-adic non-abelian Hodge theory. Examine irregular loci in Emerton-Gee stacks, K-theory of complex numbers, and mirror symmetry connections to the Breuil-Mezard conjecture. Investigate tangent bundles in p-adic geometry, pro-etale cohomology of rigid-analytic spaces, and unified theories of canonical heights on abelian varieties. Study Hodge theory for non-Archimedean analytic spaces, converses to Eisenstein's last theorem, and motives of Hitchin systems. Learn about the Fargues-Fontaine de Rham stack, generalizations of Ohta's theorem for holomorphic modular forms, and inertia stacks with gerbes and intersection cohomology. Discover new tensor categories, higher coherent cohomology in weight one, and Malle's conjecture for function fields. Explore moduli spaces with abelian motives, plectic Lie algebra actions on cohomology of Hilbert modular varieties, and strongly compatible systems associated to abelian varieties. Investigate higher singularities in positive characteristic, motivic realization of rigid local systems on curves via geometric Langlands, restriction maps in cohomology, refined topological Hochschild homology over ku, Habiro cohomology, and Frobenius lifting with geometric theories of companion forms.
