Title: Spherical functions on spherical varieties I. Abstract: I will introduce the Gross-Prasad conjecture and its enhanced form- Ichino-Ikeda conjecture. I will then introduce the general period conjecture made by Sakellaridis-Venkatesh, we will see […]
Title: Bulk-edge correspondence and an alternative proof of Bott periodicity theorem via Quot schemesAbstract: The study of topological matter is one example of the application of algebraic topology in physics. […]
Title: Condensed abelian groups II Abstract: In the previous talk, we learned about how k-Condensed Abelian Groups are abelian categories of an especially nice sort. In this talk, I will […]
Title: Rigid-analytic analogue of Artin-Grothendieck vanishing Abstract: The classical theorem of Andreotti and Frankel says that any Stein complex manifold has homotopy type of a CW complex of real dimension […]
Title: Decategorified Heegaard Floer theory and actions of both E and FAbstract: I will outline a relative of decategorified bordered sutured Heegaard Floer homology in which the vector spaces assigned […]
Title: Carleson ε^2 conjecture in higher dimensionsAbstract: I will talk about a joint work with Xavier Tolsa and Michele Villa on a higher dimensional analogue of the Carleson ε^2 conjecture. In this […]
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. […]
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 […]
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, […]
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 […]
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 […]