Title: Differential topology for diamonds Abstract: This is a gentle introduction to a new theory assigning Tangent Bundles to many non-classical objects in p-adic geometry, including the period domains and covering spaces that arise naturally when studying the p-adic cohomology of p-adic varieties. We work in Scholze’s category of diamonds, which provides a robust framework […]
Title: Coherence for pseudo symmetric multifunctors and applications to $K$-theoryAbstract: Multicategories where introduced by Elmendorf and Mandell in homotopy theory as an alternative way to encode multiplicative structures in the absence of symmetric monoidal structures. In a sense, they allow us to talk about multilinear maps even when we can't talk about tensor products. This […]
Title: Singularities in minimal submanifoldsAbstract: In the last few years there have been significant developments in techniques used to understand singularities within minimal submanifolds. I will discuss this circle of ideas and explain how they enable us to reconnect the study of geometric singularities with more classical PDE techniques, such as those used in unique continuation.
Title: On cohomology of BG.Abstract: Cohomology of classifying space/stack of a group G is the home which resides all characteristic classes of G-bundles/torsors. In this talk, we will try to explain some results on Hodge/de Rham cohomology of BG where G is a p-power order commutative group scheme over a perfect field of characteristic p, in terms of […]
Title: Kudla-Rapoport conjecture at bad reduction primes Abstract: The Kudla-Rapoport conjecture is a local analogue of arithmetic Siegel-Weil formula which relates arithmetic intersections of special cycles with derivatives of local densities. The original conjecture is formulated when the underlying Rapoport-Zink space has good reduction and proved by Chao Li and Wei Zhang. However, it is […]
Title: Laumon sheaf and the mod p Langlands program for GL_2 of a finite degree extension of Qp Abstract: Let E be a finite degree extension of Qp. Given a mod p representation of the absolute Galois group of E we construct a sheaf on a punctured absolute Banach-Colmez space that should give the first […]
Title: Towards a (3+1)-dimensional TQFT from TMFAbstract: I will discuss work in progress, joint with Sergei Gukov, Lennart Meier, and Du Pei, concerning a construction of a 4-manifold invariant using the theory of topological modular forms, and TQFT properties of this invariant. This is a mathematical construction related to a particular instance of the Gukov-Pei-Putrov-Vafa […]
Title: On the strong Sarkisov Program.Abstract: In this talk, I will explain some results about factorizing a birational map between Mori fibre spaces into Sarkisov links, such that the invariants of Sarkisov will decrease. I will explain that such problem is closely related to the termination of certain log flips in lower dimension.
Title: On the vanishing of Selmer groups for odd orthogonal Galois representations Abstract: Let $pi$ be a cuspidal automorphic representation of $Sp_2n$ over $mathbb{Q}$ which is holomorphic discrete series at infinity, and $chi$ a Dirichlet character. Then one can attach to $pi$ an orthogonal $p$-adic Galois representation $rho$ of dimension $2n+1$. Assume $rho$ is irreducible, […]
Title: Introduction to the relative Langlands program, with open problems, I.Abstract: This will be the first of a few talks introducing the "relative" Langlands program, with a view towards open problems, both concrete and speculative.