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## WS 2017/2018

### 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)

##### From Toric Varieties to Topos Points - A brief Introduction to the Geometry of Monoids

In this talk, we will give a very short and non-formal introduction to toric varieties and then move on to monoid schemes, which enable us to generalise the former. It will end with the introduction of a new type of "geometry" that one can do with monoids, where prime ideals will be replaced with topos points. These two construcitons agree in the finitely generated case, but already in the simplest non-finitely generated case, there are significantly more topos points than prime ideals. This might be especially interesting for the multiplicative monoids of commutative rings.

### 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.