Title: Compatibility of canonical ell-adic local systems on Shimura varieties Abstract: In his 1979 Corvallis paper, Deligne uses a modular interpretation to construct canonical models of Shimura varieties of Hodge type, and suggested a dream that all Shimura varieties with rational weight should be moduli spaces of motives over number fields. Outside of the abelian […]
Title: The stability of irrotational shocks and the Landau law of decay. Abstract: We consider the long-time behavior of irrotational solutions of the three-dimensional compressible Euler equations with shocks, hypersurfaces of discontinuity across which the Rankine-Hugoniot conditions for irrotational flow hold. Our analysis is motivated by Landau's analysis of spherically-symmetric shock waves, who predicted that at large times, […]
Title: Decategorifying the singular support of coherent sheaves Abstract: The microlocal homology is a family of chain theories that interpolates between the Borel–Moore homology and singular cohomology of a complex variety in the case when that variety is singular and Poincaré duality fails. Such a device allows one to speak of the singular support […]