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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.