Title: The mathematics of quantum mechanics The development of quantum mechanics in the early 20th century was a revolution in physics, and had a transformational impact on mathematics, as well. Even as we still grapple with the interpretations of the theory, its mathematical foundations are rigorous, and rooted in simple concepts of linear algebra. I […]
Title: CohomologyAbstract: Our goal in this talk is to recover the classical sheaf cohomology on topological spaces from related condensed set and condensed abelian groups. I will also discuss some infinity category theory, because from some point of view, that is where the actual story of derived category and cohomology happens.
Title: Igusa stacks and cohomology of Shimura varieties Abstract: Cohomology of Shimura varieties has drawn interest from number theory and representation theory. Following ideas developed by Caraiani-Scholze, Koshikawa, Santos, Hamann-Lee, I will explain how vanishing type of results for the generic part in the cohomology of Shimura varieties with torsion coefficients can be obtained, using […]
Title: Introduction to the Nonvanishing Hypothesis for Modular Symbols at InfinityAbstract: By "modular symbols" we will mean the integrals of cohomology classes of an arithmetic group over certain cycles on the corresponding locally symmetric space. These integrations turn out to be closely related to special values of L-functions associated to the automorphic forms which give […]
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 […]