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 to surfaces S with corners have actions of the full psl(1|1) (with both E and F) for smooth circles in the boundary of S, and […]
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 work, we characterise tangent points of certain domains in Euclidean space via a novel "spherical" square function which measures whether the common boundary of the […]
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 […]