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## WS 2018/2019

### 30.10.2018 um 16:15 Uhr in 69/125:

#### Markus Wageringel (Universität Osnabrück)

##### Moment ideals of local Dirac mixture

We study a special case of finite mixture models, the Dirac local mixtures, from an algebraic and geometric point of view, highlighting connections to algebraic statistics, symmetric tensor decomposition and signal processing. We focus on the moment varieties of first order local mixtures, providing generators for the ideals and showing a connection to moment ideals of Pareto distributions. Further, we consider mixture models of these distributions and investigate the problem of recovering the parameters of such a distribution from its moments.

This is joint work with Alexandros Grosdos Koutsoumpelias.

### 06.11.2018 um 16:15 Uhr in 69/125:

#### Dominik Nagel (Universität Osnabrück)

##### Condition numbers of Vandermonde matrices with nearly-colliding nodes

The condition number of rectangular Vandermonde matrices with nodes on the complex unit circle is important for the stability analysis of algorithms that solve trigonometric moment problems, e.g. Prony’s method. In the univariate case and with well-separated nodes, this condition number is well understood, but if nodes are nearly-colliding, the situation becomes more complicated. After recalling Prony’s method, results for the condition number of Vandermonde matrices with pairs of nearly-colliding nodes are presented.

Joint work with: Stefan Kunis.

### 12.11.2018 um 14:15 Uhr in 69/E15 :

#### Emily King (Universität Bremen)

##### Combinatorics and Discrete Geometry in (Hilbert Space) Frames

Frames are collections of vectors in Hilbert spaces which have reconstruction properties akin to orthonormal bases. In order for such a representation system to be robust in applications, one often asks that the vectors be geometrically spread apart; that is, the pairwise angles between the lines they span should be as large as possible. It ends up that structures in algebraic combinatorics, like difference sets and balanced incomplete block designs (BIBDs), can be used in different ways to construct optimal configurations. Furthermore, the linear dependencies of the vectors are often encoded as BIBDs, like affine geometry. In this talk, these and other connections between frames and algebraic combinatorics, combinatorial design theory, algebraic graph theory, and more will be presented. A couple of open conjectures will also be discussed, with one in particular possibly being amenable to combinatorial methods. Frames, difference sets, BIBDs, and affine geometry will be defined and explained, making at least part of the talk accessible to a more general audience.

### 27.11.2018 um 16:15 Uhr in 69/125:

#### Lorenzo Venturello (Universität Osnabrück)

##### Balanced triangulations on few vertices

A natural and challenging problem in combinatorial and computational topology asks for the minimum number of vertices needed to triangulate a certain manifold. Moreover since in dimension greater than 2 the number of vertices does not uniquely determine the number of higher dimensional faces, one can ask what conditions are posed on those by the topology. In this talk we focus on the family of balanced simplicial complexes, that is *d*-dimensional complexes whose underlying graph is *(d+1)*-colorable, and we exhibit balanced triangulations of surfaces and 3-manifolds on few vertices which are the result of an implementation of local flips preserving the coloring condition. This serves as an excuse to give an overview of classical results on face enumeration, both in the general and in the balanced setting.

### 18.12.2018 um 16:15 Uhr in 69/125:

#### Binh Hong Ngoc (Universität Osnabrück)

##### Expected Mean Width of Randomized Integer Convex Hull

The randomized integer convex hull is defined as the convex hull of lattice points inside a convex body on a random lattice.

We investigate the mean width of this polytope, in attempt to study its intrinsic volumes. The behaviour of mean width is presented when the given convex body is smooth. In the planar case, we also discuss some estimates if the given convex body is a polygon. Joint work with Matthias Reitzner

### 29.01.2019 um 16:15 Uhr in 69/125:

#### Jens Grygierek (Universität Osnabrück)

##### Central Limit Theorem, Central Limit Theorem, Central Limit Theorem and Multivariate Central Limit Theorem

The intrinsic volumes and the components of the f-vector of random polytopes arising as the convex hull of a Poisson point process on a smooth convex body have been studied extensively in the univariate cases.

We extend these results using floating bodies and the Malliavin-Stein-Method to establish central limit theorems for continuous and motion invariant valuations, the total intrinsic volume functional and especially the remarkable oracle estimator for the volume of a convex body derived by Baldin and Reiß (2016).

Finally we obtain a multivariate limit theorem for the intrinsic volumes and the f-vector of our random polytope altogether.