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## Current Lectures and Events

#### Advanced Applied Analysis Seminar for Degree Candidates

#### Advanced Stochastics Seminar for Degree Candidates

#### Advanced Algebra Seminar for Degree Candidates

### 19.06.2018 um 16:15 Uhr in 69/125:

#### Alexandros Grosdos Koutsoumpelias (Universität Osnabrück)

##### The Algebra of Local Mixtures

We study local mixtures of Dirac distributions and show that they possess nice algebraic properties, highlighting connections between algebra, statistics and geometry. In particular, we study the moment variety, the algebraic variety defined by the moments of these distributions, and characterize it by providing defining equations. Further, we consider mixtures of these distributions and investigate the problem of recovering the parameters of such a distribution from its moments.

This is based on an upcoming paper with Markus Wageringel.

### 26.06.2018 um 16:15 Uhr in 69/125:

#### Bernd Schober (Gottfried Wilhelm Leibniz Universität Hannover)

##### A polyhedral characterization of quasi-ordinary polynomials

The objects that we study in this talk are irreducible polynomials with coefficients in the ring of formal power series in several variables over a field of characteristic zero. Such a polynomial is called quasi-ordinary if its discriminant is a monomial times a unit. The goal of my talk is to present a construction of an invariant which detects whether a given polynomial is quasi-ordinary. The construction uses a weighted version of Hironaka's characteristic polyhedron and successive embeddings of the singularity defined by the polynomial in affine spaces of higher dimensions. In this context we will meet Teissier's notion of overweight deformations of toric varieties which appear in his program for locally resolving singularities with a single toric morphism. Finally, I will briefly mention an extension to the positive characteristic case.

#### Seminar of the Research Training Group "Combinatorial Structures in Geometry“

### 05.06.2018 um 16:15 Uhr in 69/125:

#### Jan Marten Brunink (Universität Osnabrück)

##### Combinatorics of subdivisions of simplicial complexes

I will discuss invariants of subdivisions of simplicial complexes as for example their *h*-vecto I will be interested in possible combinatorial interpretations of these invariants, in particular for the barycentric subdivision of the simplex as well as its second barycentric subdivision.

### 12.06.2018 um 16:15 Uhr in 69/125:

#### Jens Grygierek (Universität Osnabrück)

##### The Journey Project

I will take you on a small journey starting at the Central Limit Theorem for Intrinsic Volumes of random polytopes over nice valuations to the motivation to proove a multivariate Central Limit Theorem for the Intrinsic Volumes and the F-Vector of random polytopes (at the same time!).