Abstracct:
Let p be a prime and n a positive integer. On the one hand, one can consider representations on characteristic p vector spaces of the topological group GL_n(Q_p), where Q_p is the field of p-adic integers. On the other hand, one can consider representations on characteristic p vector spaces of dimension n of the absolute Galois group of Q_p. We will illustrate a conjectural duality between these two kinds of representations, in the…
Die Vorlesung hält Prof. Ingrid Daubechies. Prof. Daubechies ist James B. Duke Professor an der Duke University und war davor Professorin und Direktorin des Fachbereichs Mathematik der Princeton University. Die von ihr geleisteten fundamentalen Beiträge zur Theorie und Anwendung von Waveletmethoden ist in vielen Bereichen der angewandten Mathematik bis hin zu konkreten technischen Umsetzungen von fundamentaler Bedeutung. Für Ihre Arbeit erhielt…
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…
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…
