FG Diskrete Mathematik / Geometrie

7 Items

Recent Submissions
Subspace concentration of geometric measures

Pollehn, Hannes (2019)

In this work we study geometric measures in two different extensions of the Brunn-Minkowski theory. The first part of this thesis is concerned with problems in Lp Brunn-Minkowski theory, that is based on the concept of p-addition of convex bodies, which was first introduced by Firey for p = 1 and later considered for all real p by Lutwak et al. The interplay of the volume and other functionals ...

Tropicalization of del Pezzo surfaces

Ren, Qingchun ; Shaw, Kristin ; Sturmfels, Bernd (2016-03-30)

We determine the tropicalizations of very affine surfaces over a valued field that are obtained from del Pezzo surfaces of degree 5, 4 and 3 by removing their (-1)-curves. On these tropical surfaces, the boundary divisors are represented by trees at infinity. These trees are glued together according to the Petersen, Clebsch and Schläfli graphs, respectively. There are 27 trees on each tropical ...

Matroidal subdivisions, Dressians and tropical Grassmannians

Schröter, Benjamin (2018)

In dieser Arbeit untersuchen wir verschiedene Aspekte von tropischen linearen Räumen und deren Modulräumen, den tropischen Grassmannschen und Dressschen. Tropische lineare Räume sind dual zu Matroidunterteilungen. Motiviert durch das Konzept der Splits, dem einfachsten Fall einer polytopalen Unterteilung, wird eine neue Klasse von Matroiden eingeführt, die mit Techniken der polyedrischen Geomet...

Algebraic statistics of Gaussian mixtures

Améndola Cerón, Carlos Enrique (2017)

In this work we study the statistical models known as Gaussian mixtures from an algebraic point of view. First, we illustrate how algebraic techniques can be useful to address funda- mental questions on the shape of Gaussian mixture densities, namely the problem of determining the maximum number of modes a mixture of Gaussians can have, depending on the number of components and the dimensi...

Computer vision and computer algebra

Wagner, André (2017)

In Multiview-Geometrie, einem Teilgebiet der Computer-Vision, werden Bilder mit Kameras von 3D-Objekten aus verschiedenen Perspektiven aufgenommen. Diese Arbeit studiert Multiview-Geometrie mit Methoden aus der Computer-Algebra. Hauptprobleme des Maschinellen Sehens sind die Objektrekonstruktion und die Bestimmung der Kameraparameter. In diesen beiden fundamentalen Fragestellungen erzielen wir ...

Combinatorics of tropical linear programming

Loho, Georg (2017)

The main topic of this work is the study of systems of inequalities where only the operations 'min' and '+' are used and which we call tropical linear inequality systems. An important algorithmic problem is to determine a point which fulfills all the inequalities. This problem, referred as the tropical feasibility problem, occurs in connection with scheduling as well as mean payoff games. It is...

DGD gallery: storage, sharing, and publication of digital research data

Joswig, Michael ; Mehner, Milan ; Sechelmann, Stefan ; Techter, Jan ; Bobenko, Alexander I. (2016)

We describe a project, called the DGD Gallery, whose goal is to store geometric data and to make it publicly available. The DGD Gallery offers an online web service for the storage, sharing, and publication of digital research data.