Wochenplan des Fachbereichs Mathematik und Informatik
Christopher Deninger (WWU Münster): Topological spaces attached to systems of Diophantine equations. (Oberseminar Topologie)
Monday, 21.10.2019 14:00 im Raum SRZ 216
We attach some pretty gruesome topological spaces to systems of Diophantine equations. These spaces are equipped with an action of the multiplicative group of positive rational numbers and we discuss relations between the topology and the group action on the one hand and the arithmetic of the Diophantine equations on the other.
Oberseminar Differentialgeometrie: Elena Mäder-Baumdicker (Darmstadt): Willmore spheres are unstable
Monday, 21.10.2019 16:15 im Raum SR4
Abstract: I will explain what the Willmore Morse Index of unbranched Willmore spheres in Euclidean three-space is and how to compute it. A consequence of that computation is that all unbranched Willmore spheres are unstable (except for the round sphere). This talk is based on work with Jonas Hirsch.
Sahana Balasubramanya (Münster): Hyperbolic structures on groups. (Geometric Group Theory Seminar)
Wednesday, 23.10.2019 14:15 im Raum SRZ 216
For any group G, I will define the set of hyperbolic structures on G, denoted H(G), which consists of equivalence classes of (possibly infinite) generating sets of G such that the corresponding Cayley graph is hyperbolic. Alternatively, one can define hyperbolic structures in terms of cobounded G-actions on hyperbolic spaces. Of special interest is the subset AH(G) of H(G) , which consists of acylindrically hyperbolic structures on G, i.e. hyperbolic structures corresponding to acylindrical actions.
I will discuss basic properties of these posets such as cardinality, existence of extremal elements, results about hyperbolic structures induced from hyperbolically embedded subgroups of G and accessibility. Lastly I will talk about some recent work regarding quasi-parabolic structures.
Pierre Touchard: Burden in exact sequences of abelian groups
Thursday, 24.10.2019 11:00 im Raum SR 1D
In model theory, the burden is a notion of dimension for NTP2 structures, which form a relatively tame class of first order structures. Chernikov and Simon (2016) consider exact sequences of abelian groups A -> B -> C, and modulo the hypothesis that B/nB is finite for all integers n, they prove a quantifier elimination result. Then, they compute the burden in a particular case: if the burden of A and burden of C are equal to 1, so is the burden of A->B->C. However, the condition of finite classes modulo n is restrictive. For
instance, it is known that abelian groups with finite classes modulo n are exactly the ones of burden 1 (Jahnke, Simon, Walsberg). Using a new quantifier elimination result of Aschenbrenner, Chernikov, Gehret and Ziegler, one can show in general that the burden of a pure exact sequence of abelian groups is given by the following formula: bdn(A->B->C) = max_n (bdn(A/nA) + bdn(nC)). I will present some examples and a sketch of the proof. I will also present some
applications of this result.
Kolloquium Wilhelm Killing: Prof. Dr. Marc Levine (Duisburg-Essen): GWGW theory
Thursday, 24.10.2019 16:30 im Raum M5
Abstract: We will describe recent work constructing refinements to the Grothendieck-Witt ring of a number of integer-valued invariants found in enumerative geometry and Gromov-Witten theory. This includes: Euler characteristics, Riemann-Hurwitz formulas, counts of lines on hypersurfaces and counts of rational curves on surfaces.