Title: Frieze Patterns Abstract: As we are in the midst of a cold, dark winter... there is no better time to learn about frieze patterns. Frieze patterns were first defined by mathematicians to classify certain symmetries in ancient art and architecture. In this talk, we will explore arrays of mathematical objects that obey these classified frieze pattern […]
Title: The role of curvature in the production of sound: Music, Geometry and BeyondAbstract: When a string vibrates, it produces different pitches depending on its length. This is how guitarists can play several notes using only one string. But what happens when we have surfaces or 3D objects that vibrate, like when playing a flute, […]
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 […]
Title: L^p bounds for spectral projectors on hyperbolic surfacesAbstract: In this talk I will present L^p boundedness results for spectral projectors on hyperbolic surfaces, focusing on the case where the spectral window has small width. I will show that the negative curvature assumption leads to improvements over the universal bounds of C. Sogge, thus illustrating […]
Title: Selmer groups, p-adic L-functions and Euler Systems: A new Framework Abstract: Selmer groups are key invariants attached to p-adic Galois representations. The Bloch—Kato conjecture predicts a precise relationship between the size of certain Selmer groups and the leading term of the L-function of the Galois representation under consideration. In particular, when the L-function does […]
Title: Singularity formation in incompressible fluids. Abstract: I will discuss a recent example of singularity formation in the 3d Euler equation. This is based on work joint with Federico Pasqualotto.
Title: TBA
Title: Bipartite Euler SystemsAbstract: I will give an example-based introduction to bipartite Euler Systems, starting with the construction in the case of Heegner points by Bertolini--Darmon from the early 2000's. I'll discuss the main obstacles in extending such methods to other settings, and survey some of the new constructions we have seen in the last […]