Termine

Further information

In the previous talk, we introduced the notion of geometric modularity in the sense that $\rho$ arises from a mod $p$ Hilbert modular form, and algebraic modularity in the sense that $\rho$ arises in the mod $p$ cohomology of a Shimura curve. In this talk, I will explain the idea of the proof that geometric modularity implies algebraic modularity of the same weight. The main strategies are the liftability of mod p Hilbert cusp forms, using weight-shifting operators, and the description of the Goren-Oort stratification.

wissenschaftliches Kolloquium am IDMI

The Bose gas is an important model in quantum statistical mechanics. In this talk, I introduce a probabilistic representation going back to Feynman, given by a reference measure and an interaction. I will first review some results on the reference process. I will then discuss recent results and techniques regarding the construction of Gibbs measures and large deviations when interaction is present.

Abstract: The answer that I will propose is a higher categorical structure in symplectic geometry that includes all Fukaya categories and geometric functors between them. Its highly involved algebraic and analytic details are the topic of joint work with Nate Bottman. However, its basic structure can be understood as a natural -- yet not previously studied -- extension of the category of topological spaces and continuous maps. So the goal of this talk is to make broadly accessible the two underlying ideas: The notion of quilts (collections of maps related by ``seam conditions'') and the string diagram approach to constructing and making sense of 2-categories.