[Facets-of-complexity] Invitation to Monday Lecture & Colloquium -November 18th 2019

[Ita Brunke <i.brunke@inf.fu-berlin.de>]

You are cordially invited to our next Monday Lecture & Colloquium on November 18th at 14:15 h & 16:00 h at TU Berlin.

Location:

Room MA 041 - Ground Floor
Technische Universität Berlin
Straße des 17. Juni 136
10623 Berlin 

Time: Monday, November 18th - 14:15 h

Lecture: Matthias Reitzner (Universität Osnabrück)

Title: Stars of Empty Simplices

Abstract:

Consider an n-element point set in general position in d-dimensional space. For a k-element subset the degree is the number of empty d-simplices with this k-set as base. We investigate the maximal degree of a random point set consisting of n independently and uniformly chosen points from a compact set.

Coffee & Tea Break :

Room MA 316 - Third Floor [British Reading]

Time: Monday, November 18th - 16:00 h s.t.

Colloquium: Ansgar Freyer (Technische Universität Berlin)

Title: Discrete analogs of an inequality by Meyer

Abstract:

In 1988, Mathieu Meyer presented a lower bound on the volume of a convex body in terms of the volumes of its sections with the coordinate hyperplanes.
Our aim is to "discretize" this inequality by replacing the volume by the lattice point enumerator. It turns out that such a discrete analog cannot exist for general convex bodies. Moreover, it will not imply its continuous counterpart.
We prove inequalities for the case of o-symmetric bodies (using arithmetic progressions) and unconditional bodies (by proving a universal bound for the lattice point enumerator of unconditional lattice polytopes). Moreover, the talk will touch on a reverse inequality and other related problems.