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: 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: 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: 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 […]