Title: Torsion vanishing for some Shimura varietiesAbstract: We will discuss joint work with Linus Hamann on generalizing the torsion-vanishing results of Caraiani-Scholze and Koshikawa for the cohomology of Shimura varieties. We do this by applying various geometric methods to understand sheaves on Bun_G, the moduli stack of G-bundles on the Fargues-Fontaine curve. Our method showcases that […]
Title: Computer Assisted Proof of Finite Time Singularity of the 3D Euler Equations Abstract: Whether the 3D incompressible Navier-Stokes equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In the first talk, we will present some new numerical evidence that the 3D Navier-Stokes […]
Title: The inverse spectral problem for ellipses Abstract: This talk is about Kac‘s inverse problem from 1966: "Can one hear the shape of a drum?" The question asks whether the frequencies of vibration of a bounded domain determine the shape of the domain. First we present a quick survey on the known results. Then […]
Title and abstract TBA
Plancherel formula 2
Title: What is an automorphic representation? Abstract: Andrew Wiles' famous proof of Fermat's last theorem was crucially based on constructing a mysterious connection between two classes of mathematical objects: "modular forms" and "elliptic curves". However, if you try looking up what a modular form actually is, you'll find an elementary but very unmotivated definition involving functions on […]
Title: Boundary behavior of the Allen-Cahn equation and the construction of free boundary minimal hypersurfacesAbstract: In the late 70s, the work of Modica, Mortola, De Giorgi, and many others established deep connections between the Allen-Cahn equation, a semi-linear elliptic equation arising in the van der Waals-Cahn-Hilliard theory of phase transitions, and minimal hypersurfaces, i.e. critical […]
Title: Liquid & gaseous modules
Title: Isotrivial fibrations of hyper-Kähler manifolds.Abstract: A Lagrangian fibration of a projective hyper-Kähler manifold is called isotrivial if its smooth (abelian variety) fibers are all isomorphic to each other. Given an isotrivial fibration of a HK manifold f : X -> B with at least one rational section, we prove the following four descriptions of the fibration: […]
Title: Twisted Gan-Gross-Prasad conjecture and arithmetic fundamental lemma Abstract: The twisted Gan-Gross-Prasad (GGP) conjecture opens a way of studying (a twist of) central Asai L-values via descents and period integrals. Firstly, I will prove new cases of twisted GGP conjecture (joint work with Weixiao Lu and Danielle Wang), based on the relative trace formula approach […]
Title and abstract TBA