FB 6 Mathematik/Informatik

Institut für Mathematik


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SS 2017

11.04.2017 um 16:15 Uhr in 69/125:

Lorenzo Venturello (Universität Osnabrück)

Balanced moves on combinatorial manifolds

A theorem by Pachner states that an equivalent condition for two combinatorial manifolds to be PL homeomorphic is to be connected by a sequence of local moves called bistellar flips.Recently Izmestiev, Klee and Novik introduced the notion of cross-flip as a balanced analog of such moves and established a similar equivalence. Moreover Pachner showed that any two PL homeomorphic manifolds with boundary can be connected by a sequence of shellings and inverse shellings. In this talk, I will speak about the balanced analog of this theorem (as suggested by Izmestiev, Klee and Novik) and provide the first steps towards its proof.

18.04.2017 um 16:15 Uhr in 69/125:

Konrad Voelkel (Universität Osnabrück)

An Algebraic Geometer's Sphere

We will give an answer to the question what an algebro-geometric sphere is and why such an object is worth studying. This gives us an excuse to motivate the categorical and functorial language for mathematics, which will occupy us for most of the time. We will give precise definitions of these notions, examples and explanations and this will not require any prerequisites in the subject.

24.04.2017 um 16:15 Uhr in 69/125:

Seth Sullivant (North Carolina State University)

Algebraic Geometry of Gaussian Graphical Models

Gaussian graphical models are statistical models widely used for modeling complex interactions between collections of linearly related random variables.  A graph is used to encode recursive linear relationships with correlated error terms.  These models a subalgebraic subsets of the cone of positive definite matrices, that generalize familiar objects in combinatorial algebraic geometry like toric varieties and determinantal varieties.  I will explain how the study of the equations of these models is related to matrix Schubert varieties.  This is joint work with Alex Fink and Jenna Rajchgot.

16.05.2017 um 16:15 Uhr in 69/125:

Jonathan Steinbuch (Universität Osnabrück)

Tight closure and continuous closur

Tight closure, was designed by Hochster and Huneke, to tackle problems related to diverse topics such as the Cohen-Macaulay-Property or the Briançon-Skoda-theorem. We discuss a connection of it with two other closure operations introduced by Brenner. Our main theorem shows that the tight closure of an ideal is contained in its axes closure in the case of normal rings. By reduction modulo p this result extends also to characteristic 0. Under some further assumptions this gives the Corollary that the tight closure is also contained in the continuous closure.

23.05.2017 um 16:15 Uhr in 69/125:

Markus Wageringel (Universität Osnabrück)

Tensor decomposition and Prony's method

A higher-order tensor can be seen as a generalization of a matrix, a multi-dimensional array. The problem of decomposing such a tensor into a sum of rank-1 tensors then generalizes the Singular Value Decomposition of a matrix, an important tool in numerical linear algebra. After introducing the tensor decomposition problem, we relate it to Prony's method, a tool for recovering point measures from moments with applications in signal processing.