Title: Recent Progress on Fractional GJMS OperatorsAbstract: The Fractional GJMS operators are one-parameter family of conformally invariant operators, defined by the renormalized scattering operators on the conformal infinity of Poincare-Einstein Manifolds. These operators provide a bridge to transfer the information of interior Einstein geometry to the boundary conformal geometry. In this talk, I will first […]
Title: Equivariant birational geometry.Abstract: I will discuss new invariants of actions of finite groups on algebraic varieties and their applications (joint with A. Kresch, I. Cheltsov and Zh. Zhang).
Title: Why do cusp forms exist? Abstract: I will begin this talk by reviewing the Eichler-Shimura isomorphism between the space of cusp forms of weight k and level N, and a certain cohomology group. Shimura called this cohomology group as parabolic cohomology. In the context of automorphic forms on higher groups, such a cohomology group takes the form […]
Title: Stone duality between condensed mathematics and algebraic geometry Abstract: One classical incarnation of Stone duality is an anti-equivalence between the categories of profinite sets and Boolean algebras respectively. In this talk, we will discuss how this can be extended to a fully faithful embedding of condensed sets into fpqc sheaves over any base field. […]
Title: Integer Decomposition Property of lattice polytopes Abstract: Given a polytope (higher dimensional polygon) P and a non-negative integer k, we can multiply every point of P by k to obtain another polytope kP. One of the properties P can have is the integer decomposition property: if x is a point in kP, then there […]