FB 6 Mathematik/Informatik

Institut für Mathematik


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WS 2019/2020

10.12.2019 um 13:00 Uhr in Raum 69/E15  -Uni-GK-

Stephan Bussmann 

An exploration of the truncated cylinder model

Consider a Boolean model and a random direction movement scheme. Given a fixed time horizon T>0, we model these movements via cylinders reaching from the original plane of the boolean model at time 0 to an affine plane at time T. We study the asymptotic behavior of functionals of the union set of cylinders Z restricted to a window of observation W, which has its volume tending to infinity. Considered functionals include the 3-dimensional volume of the intersection of Z and W and its Euler characteristic.

17.12.2019 um 12:00 Uhr in Raum 69/E15

Jens Grygierek

Random Geometric Structures

In the first part, we use a stationary Poisson point process to construct two random simplicial complexes, the random Vietoris-Rips complex and the random Cech complex, that are rich enough to realize any compact topological manifold, at least up to homotopy equivalence.
In the second part, we investigate the random Vietoris-Rips complex constructed from a stationary Poisson point process on a d-dimensional compact set using the uniform norm.
Opposed to most of the existing literature in which the focus lies on random geometric graphs in the fixed dimensional case, we will generalize this model by investigating the asymptotic distributional behavior of the f-vector if the intensity as well as the space dimension d tend to infinity simultaneously.
It turns out, that the phase-transition phenomenon occurs also in the components of the f-vector of the random Vietoris-Rips complex in the fixed and high-dimensional cases.

07.01.2020 um 13:00 Uhr in Raum 69/E15 -Uni GK-

Tobias Oelschlägel

Approximationsalgorithmen für Storage Loading Probleme

14.01.2020 um 13:00 Uhr in Raum 69/E15  -Uni GK-

Sven Boge

TBA

21.01.2020 um 12:00 Uhr in Raum 69/E15

Grace Itunuoluwa Akinwande

Poisson Limit Theorems for Z+-valued U-statistics

We give an abstract PLT for U-statistics with positive integer values, and for functionals related to the f-vector of a random simplicial complex in particular in particular

28.01.2020 um 13:00 Uhr in Raum 69/E15  -Uni-GK-

Alexander Nover

Cut Polytope von Bicycle Wheels

11.02.2020 um 12:00 Uhr in Raum 69/E15

Binh Hong Ngoc

Surface area of randomized integer convex hull

We investigate the surface area of randomized integer convex hull inside a smooth convex body. We give the asymptotic expectation of surface area when the convex body is very large.