Title: Highly Connected 7-manifolds, Non-negative Curvature and the Linking FormAbstract: Closed manifolds admitting non-negative sectional curvature are not very well understood and it is, at present, quite difficult to obtain examples with interesting topology. All known examples depend in some way on two basic facts: First, compact Lie groups admit a bi-invariant metric (hence, non-negative […]
Title: Frobenius-type results on submanifolds and currentsAbstract: The question of producing a foliation of the n-dimensional Euclidean space with k-dimensional submanifolds which are tangent to a prescribed k-dimensional simple vectorfield is part of the celebrated Frobenius theorem: a decomposition in smooth submanifolds tangent to a given vectorfield is feasible (and then the vectorfield itself is […]
Title: Locally compact abelian groups
Title: A non-Archimedean characterization of local K-stability.Abstract: Log Fano cone singularities are generalizations of affine cones over Fano varieties. Motivated by the study of canonical metrics on Fano varieties, there is a local K-stability theory characterizing the existence of Ricci-flat K"ahler cone metrics on log Fano cone singularities. In this talk, we aim to give a non-Archimedean […]
Title: Fourier Interpolation and the Weil Representation Abstract: In 2017, Radchenko-Viazovska proved a remarkable interpolation result for even Schwartz functions on the real line: such a function is entirely determined by its values and those of its Fourier transform at square roots of integers. We give a new proof of this result, exploiting the fact […]
Title: Springer resolution and representation theoryAbstract: Given a connected complex reductive group G, I would like to explain how doing geometry on the Springer resolution and the Steinberg variety allows one to give a spectral description (i.e. irreducible representations) of the Weyl group of G.
Title: Interpolation for Brill–Noether Curves Abstract: The interpolation problem is one of the oldest problems in mathematics. In its most broad form it asks: When can a curve of a given type be passed through a given number of general points? In this two-part talk, we will discuss our recent joint work that completely solves […]
Title: Interpolation for Brill–Noether Curves Abstract: The interpolation problem is one of the oldest problems in mathematics. In its most broad form it asks: When can a curve of a given type be passed through a given number of general points? In this two-part talk, we will discuss our recent joint work that completely solves […]
Title: The unipotent categorical local Langlands correspondence. Abstract: I will discuss a conjectural categorical form of the local Langlands correspondence for p-adic groups and establish the unipotent part of such correspondence (for characteristic zero coefficient field).
Title: The unipotent categorical local Langlands correspondence. Abstract: I will discuss a conjectural categorical form of the local Langlands correspondence for p-adic groups and establish the unipotent part of such correspondence (for characteristic zero coefficient field).
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 […]