Title: Three theorems about asymptotic expansions of harmonic functions at the boundaryAbstract: Consider a harmonic function on a domain, vanishing along a part of its boundary, and a point on that part of the boundary which is asymptotically conical. I will explain that under a very mild notion of "asymptotically conical," the harmonic function has […]
Title: On the generalized Beauville decomposition.Abstract: Over 30 years ago, the work of Beauville and Deninger-Murre endowed the cohomology of an abelian scheme a (motivic) decomposition which splits the Leray filtration. This structure, now known as the Beauville decomposition, is induced by algebraic cycles obtained from the Fourier-Mukai coherent duality. In recent years, the study of Hitchin […]
Title: Huber pairs
Title: Calculus of fractions for quasicategories Abstract: A central object of interest in abstract homotopy theory is the localization of marked categories. One case of interest is when the marked category admits a "calculus of fractions". This condition was introduced by P. Gabriel and M. Zisman to construct better-behaved models for the localization. For instance, […]
Title: Potential Singularity of the 3D Navier-Stokes 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 equations seem to develop nearly […]
Title: Syzygies of Mori fibre spaces
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 […]