09.04.2019 um 16:15 Uhr in 69/125:
Dinh Le Van (Universität Osnabrück)
A Kruskal-Katona type theorem
The classical Kruskal-Katona theorem solves the shadow minimization problem, leading to a characterization of all possible face numbers of simplicial complexes. Inspired by this theorem we study a minimization problem, where the role of the shadow is replaced by the image of the action of the monoid of increasing functions. We provide a solution to this problem as well as an application to simplicial complexes. This talk, based on joint work with T. Römer, is entirely elementary.
23.04.2019 um 16:15 Uhr in 69/125:
Marcin Wnuk (Universität Osnabrück)
Negative Dependence in Numerical Integration and Discrepancy Theory
Intuitively, a randomized point set in a d-dimensional unit cube is said to be negatively dependent if the points tend not to cluster. In my talk I will present a few notions of negative dependence, as well as their applications: it turns out that negatively dependent point sets yield good quadrature nodes, and in some sense (measured by the so-called discrepancy) are highly regular.
In the end I will discuss concrete constructions of negatively dependent point sets.