Algebra and Number Theory Day: Alexander Petrov (MIT)

Gilman Hall 132

Title: Characteristic classes of p-adic local systems.Abstract: A useful tool in studying vector bundles on topological spaces or algebraic varieties is characteristic classes in cohomology, such as Chern classes. For vector bundles equipped with a flat connection, Chern classes vanish in cohomology with rational coefficients, but such bundles have a non-trivial theory of secondary characteristic classes, […]

Algebra and Number Theory Day: Mihnea Popa (Harvard)

Gilman Hall 132

Title: Hodge symmetries of singular varieties.Abstract: The Hodge diamond of a smooth projective complex variety contains essential topological and analytic information, including fundamental symmetries provided by Poincaré and Serre duality. I will describe recent progress on understanding how much symmetry there is in the analogous Hodge–Du Bois diamond of a singular variety, and the concrete ways […]

Number Theory Seminar: Carl Wang-Erickson (University of Pittsburgh)

Krieger 411

Title: Bi-ordinary modular forms Abstract: Hida theory provides a p-adic interpolation of modular forms that have an ordinary property. Correspondingly, the p-adic 2-dimensional Galois representations associated to the eigensystems of the Hecke action on these ordinary modular forms have a property known as ordinary: when restricted to a decomposition group at p, this representation is […]

Automorphic forms learning seminar: Milton Lin (JHU)

Krieger 411

Title: Review of geometric local Langlands for GL1 in mixed characteristic and  an introduction to Banach Colmez Spaces. Reference: Hansen's Beijing Lecture Notes on Categorical Local Langlands & Fargues-Scholze.

Analysis seminar: Aditya Kumar (JHU)

Krieger 205

Title: Positive scalar curvature and exotic structures on simply connected four manifolds.Abstract: We address Gromov’s band width inequality and Rosenberg’s S1-stability conjecture for smooth four manifolds. Both results are known to be false in dimension 4 due to counterexamples based on Seiberg-Witten invariants. Nevertheless, we show that both of these results hold upon considering simply […]

Algebraic Geometry Seminar: Daniel Halpern-Leistner (Cornell)

Krieger 411

Title: An intrinsic approach to moduli theoryAbstract: A central problem in algebraic geometry is to construct and study moduli spaces of objects of interesting geometric objects. The classical tool for this is geometric invariant theory, which requires you to approximate a moduli problem by an orbit space X/G for some reductive group G acting on […]