Title: The covering minima of lattice polytopes
The covering minima of a convex body were introduced by Kannan and Lovasz to give a better bound in the flatness theorem, which states that lattice point free convex bodies cannot have arbitrarily large width. These minima are similar in flavor to Minkowski's successive minima, and on the other hand generalize the covering radius of a convex body. I will speak about recent joint work with Francisco Santos and Matthias Schymura, where we investigate extremal values of these covering minima for lattice polytopes.
Title: Classification of Weyl groupoids
Abstract: Finite Weyl groupoids (these are certain simplicial arrangements in a lattice) were completely classified in a series of papers by Heckenberger and myself. However, this classification is based on two computer proofs checking millions of cases. In this talk, I want to report on recent progress in finding a shorter proof. In particular, we prove without using a computer that, up to equivalence, there are only finitely many irreducible finite Weyl groupoids in each rank greater than two.