Termine

A C*-algebra is called pure if it has good comparison and divisibility properties; more precisely, its Cuntz semigroup is almost unperforated and almost divisible. A natural question, raised at several conferences, is whether the minimal tensor product $A \otimes B$ remains pure whenever $A$ is. In this talk, we shall see results addressing this question when $B = C(X)$. We will also discuss applications to crossed products. This talk is based on two joint works: one with Vilalta, and another with Archey, Buck, Mohammadkarimi, and Phillips.

In these two talks I will present my current project on endowing a torsor structure on L-packet of the covering tori. In the first half I will talk about how to construct gerbes on the groupoid of isocrystals, and a formulation of the Langlands correspondence of sharp covering tori on the level of gerbes. In the second half I will talk about how the groupoid of isocrystals of the sharp tori can help to interpolate the L-packets of different extended pure inner forms of the covering tori, which gives rise to the desired torsor structure.

Hyperbolic conservation laws are a class of partial differential equations governing a variety of important applications from coastal flooding to supersonic aerodynamics. Simulation of hyperbolic conservation laws presents a number of challenges, such as long time scales, the ability to produce shocks, and large, geometrically complex, and potentially moving/deforming domains. Discontinuous Galerkin (DG) and finite volume (FV) methods on cut meshes are uniquely equipped to address these challenges provided they can overcome hurdles of their own: entropy stability, the small cell problem, cut cell quadrature, and, in the case of moving boundaries, interface reconstruction/tracking. In this talk I will share my research in cut DG/FV methods capable of overcoming these hurdles and recent work in adapting these methods to tracking the wet-dry front in storm surge simulation.

TBA

In 2001, Oort conjectured that generic supersingular abelian varieties of dimension at least 2 do not have automorphisms other than \pm id. We will report on the history and the recent proof of this conjecture (by Viehmann) as well as on possible generalizations (in joint work of the speakers with Fabian Schnelle) and implications.

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