Abstract: Submetries are maps between metric spaces which send balls onto balls of the same radii. They generalize Riemannian submersions and quotient maps for isometric group actions. In the talk, I will discuss topological, analytic and algebraic structural results for such maps.
If you are interested in participating online please contact Tobias Weich in order to receive the login details.
Title: Minuscule Coxeter Dressians
Abstract: Matroids combinatorially abstract independence systems and have deep connections throughout mathematics. One characterization of matroids is given by (0,1)-polytopes with edge directions in the type A root system. In this case, edges capture "symmetric exchange" between bases. Regular matroidal subdivisions of polytopes are well studied. In particular,…
Title: Counting $D_4$ extensions by multiple invariants
Abstract: Malle’s conjecture is a central question in arithmetic statistics, predicting an asymptotic formula for the number of number fields with a prescribed Galois group and bounded discriminant. Recently, such counting problems have received considerable attention. In 2022 Gundlach introduced the notion of ordering number fields by…
Many dynamical systems in fields such as neuroscience (the workings of the brain), systems biology (metabolic networks), and robotics (robot swarms) exhibit the structure of a network: they consist of nodes (neurons, proteins, robots) interconnected by edges. The specific architecture of these interactions can give rise to remarkably complex dynamics that go far beyond the behavior of individual nodes. Prominent examples include synchronization…
