Abstract: In this talk we will discuss Coxeter groups and their "Vinberg representations". These are discrete and faithful representations that are of special geometric significance. As we will show, the Zariski-closure of such representations is very restricted. This allows us to construct new examples of Zariski-dense subgroups of SL(n,Z). In particular, we will prove that, for all n at least 3, SL(n,Z) contains a Zariski-dense subgroup…
Title: Additive combinatorics and descent
Abstract: In this talk I will outline a method introduced in joint work with Peter Koymans that allowed us to settle Hilbert 10th problem for all finitely generated rings and to show that every number field has an elliptic curve of rank 1. I will also present joint work with Alexandra Shlapentokh outlining some further consequences of these results and…
Title: Quiver Grassmannians for the Bott-Samelson resolution of type A Schubert varieties
Abstract: Quiver Grassmannians are projective varieties parametrising subrepresentations of quiver representations. Their geometry is an interesting object of study, due to the fact that many geometric properties can be studied via the representation theory of quivers. In this talk, we construct a special…
Abstract: The optimal matching problem is one of the classical random optimization problems. While the asymptotic behavior of the expected cost is well understood only little is known for the asymptotic behavior of the optimal couplings - the solutions to the optimal matching problem. In this talk we show that at all mesoscopic scales the displacement under the optimal coupling converges in suitable Sobolev spaces to a Gaussian field which can be…
Title: Linear Disjointness, Relativised Cyclotomic Polynomials and Inflated G-extensions for Number Fields
Abstract: There had been many attempts to generalize cyclotomic polynomials by many authors: combinatorialapproach using MOebius Inversion, Number-Theoretic approacj=h by focussing on unitary divisors etc. Our approach takes the factorization of X^n-1 as the model and defines cyclotomic…
Abstract:
Die gymnasiale Oberstufe hat in den letzten Jahrzehnten einen stetigen Zulauf erfahren, sodass die Abiturientenquote eines Altersjahrgangs heute bei etwa 40 Prozent liegt. Dadurch nimmt sie einen immer bedeutenderen Platz im institutionalisierten schulischen Bildungsangebot ein, weshalb eine (erneute) wissenschaftliche Auseinandersetzung mit den Bildungszielen und den Wirkungen des Unterrichts in der gymnasialen Oberstufe sinnvoll…
