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)
24.11.2017 um 16:15 Uhr in 69/125:
Prof. Dr. Walter Ferrer (University of the Republic, Uruguay)
Observability: From Subgroups to Actions and Adjunctions
The exploration of the notion of observability exhibits transparently the rich interplay between
algebraic and geometric ideas in geometric invariant theory. We will talk about the concept of observable subgroup introduced in the 1960s with the purpose of studying extensions of representations from an affine algebraic subgroup to the whole group. It can be considered as an intermediate step in the notion of reductivity (semisimplicity) and it has been recently generalized to the concept of observable action of an affine algebraic group on an affine variety. We will also talk about the related concept of observable adjunction.
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.