07.11.2017 um 16:15 Uhr in 69/125:
Grace Itunuoluwa Akinwande (Universität Osnabrück)
Random Simplicial Complexes
Random simplicial complexes are higher dimensional generalizations of random graphs. In particular, the aim is to get limit theorems for the Vietoris-Rips complex. In this talk, I'll introduce the Gilbert graph and discuss previous results on it. I'll then generalize these to higher dimensional simplicial complexes.
22.11.2017 um 16:15 Uhr in 69/125:
Ilia Pirashvili (Universität Osnabrück)
28.11.2017 um 16:15 Uhr in 69/125:
Timo de Wolff (TU Berlin)
Discrete Structures Related to Nonnegativity
Deciding nonnegativity of real polynomials is a fundamental problem in real algebraic geometry and polynomial optimization, which has countless applications. Since this problem is extremely hard, one usually restricts to sufficient conditions (certificates) for nonnegativity, which are easier to check. For example, since the 19th century the standard certificates for nonnegativity are sums of squares (SOS), which motivated Hilbert’s 17th problem. A maybe surprising fact is that both polynomial nonnegativity and nonnegativity certificates re closely related to different discrete structures such as polytopes and point configurations. In this talk, I will give an introduction to nonnegativity of real polynomial with a focus on the combinatorial point of view.