Vorträge des SFB 1442

Abstract: In Appendix C of his "Anyons" paper, Kitaev introduced the notion of a "generalized Chern number" for a 2-dimensional system by diving the system in three ordered parts and measuring a signed rotational flux. This construction has since been used by several authors to measure topological non-triviality of a physical system. In recent work with Guo Chuan Thiang, we observe that the recipe provided by Kitaev can be interpreted in coarse geometry as the pairing of a K-theory class with a coarse cohomology class. A corresponding index theorem then provides a proof that the set of values of this "Kitaev pairing" is always quantized, as already argued by Kitaev. In our work, we generalize Kitaev?s definition and the corresponding quantization result to arbitrary dimensions.

Given a six functor formalism, one can parametrise the ways to twist the f_!-functors a bit without changing f^*. Using the same principles, one obtains general constructions of monodromic and gerbe-twisted sheaves. The usual construction of six functor formalisms via factorisation into classes I and P by Liu-Zheng assumes that morphism in the intersection of I and P are truncated. In joint work in progress with Will Fisher, we show that without this assumption, one can still construct a twisted six functor formalism.

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The Anti-de-Sitter (AdS) space is the analogue in Lorentzian geometry to the hyperbolic space of negative constant curvature familiar to Riemannian geometers. The study of the Anti-de-Sitter space and more generally, of solutions to the Einstein equations which ressemble the Anti-de-Sitter space has many applications in high energy physics and provides mathematicians with problems lying at the intersection of Lorenzian geometry and hyperbolic pdes. I will start with a general introduction to the study of the Einstein equations, with an emphasis on the evolution problem. I will then briefly discuss the well-posedness for wave equations, including the Einstein equations, in the case of AdS type boundaries. In the second part of the talk, I will present several results concerning the linear or non-linear perturbations of the AdS space for the vacuum Einstein equations and some related toy models.

In this talk we want to provide some insight into the everyday life of a mathematician in the world of corporates. We shall report on our experiences at d-fine GmbH, a management consulting company with an analytic and technological focus, thereby aiming to present a diverse picture: not only shall we delve into the world of databases and related evaluations via graph-theoretic techniques, but we shall also discuss topics in sustainability reporting most prominently featuring an approach to the challenging subject of modelling key invariants for biodiversity.