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 […]
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 […]
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 […]
Title and abstract TBA
Title: Complexity of actions over perfect fields Abstract: Let K be a field, let G be a reductive K-group and let X be a G-variety. When K is algebraically closed, […]
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.
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 […]
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 […]