Sprungmarken

Servicenavigation

TU Dortmund

Hauptnavigation


Bereichsnavigation

Mathematisches Kolloquium

Datum Gastredner Thema Ort
Im Rahmen des Mathematischen Kolloquiums
Im Rahmen des Oberseminars Stochastik und Analysis
21.04.2022
16.15 Uhr
Prof. Dr. Michael Voit
Fakultät für Mathematik, TU Dortmund
Freezing limits for Cauchy ensembles Mathematikgebäude, M611
Im Rahmen des Mathematischen Kolloquiums
Oberseminar Analysis, Mathematische Physik, Dynamische Systeme
14.06.2022
14.00 Uhr
Irwin Yousept
Duisburg-Essen
Recent Mathematical Challenges in Electrodynamics of Superconductivity

Zusammenfassung


In this talk, we present recent mathematical results in Maxwell variational inequalities with technological applications in high-temperature superconductivity and EM-shielding. The established well-posedness opens a way to analyze the corresponding numerical approximations, optimal design and inverse problems, which are mainly complicated by the hyperbolic Maxwell structure and the non-smooth character. Results in these directions are presented.
[Abstract]
[WWW]
M/511
Im Rahmen des Mathematischen Kolloquiums
Oberseminar Analysis, Mathematische Physik, Dynamische Systeme
14.06.2022
15.00 Uhr
Martin Lazar
Dubrovnik
Constrained LQ optimization problems with parameter dependent coefficients.

Zusammenfassung


We consider a sequence of linear-quadratic optimization problems defined in an abstract functional framework. Each problem is accompanied by the constraint of reaching a given target with some precision. We show that problems are well posed and we characterise their solutions. The main result provides the conditions under which these solutions converge to the minimizer of the limit problem. The theory can be applied to a wide range of problems: elliptic, parabolic, control ones etc. In the talk, the following examples will be presented: 1. optimal controllability of the heat equation 2. optimal solvability of the Poisson equation.
[Abstract]
M/511
Im Rahmen des Mathematischen Kolloquiums
20.06.2022
16:30 Uhr
Prof. Dr. Anja Fischer
Fakultät Wirtschaftswissenschaften, TU Dortmund
Combinatorial optimization meets facility layout problems

Zusammenfassung


Given a set of departments and the pairwise transport weights between them, the Single-Row Facility Layout Problem (SRFLP) asks for an arrangement of the departments on one side of a path such that the weighted sum of the distances between the departments is minimized. The best integer linear programming approach for the SRFLP is based on the betweenness model (Amaral, 2009).
In this talk we present new classes of inequalities for the associated betweenness polytope and show their validity using combinatorial arguments. Using a cutting plane approach allows us to solve more and larger instances of the SRFLP to optimality than the lower bounding approach of Amaral. In the second part of the talk we consider the Multi-Bay Facility Layout Problem and Facility Layouts with Pier Type Patterns which are special Combined Cell Layout Problems (CCLP). Here the path structure is more complicated. We solve these problems exactly by enumerating over all assignments of the departments to the cells and solving several CCLP with fixed-cell assignment using the betweenness model in each of the subproblems. We show how to reduce the number of distinguishable cell assignments significantly by merging two cells of type single-row.
[Abstract]
[PDF]
vorab Institutstee / -kaffee um 16.00 Uhr im Besprechungsraum M614/616
Mathematikgebäude, Hörsaal E28
Vortrag im Rahmen des Gambrinus-Fellowships
Im Rahmen des Mathematischen Kolloquiums
27.06.2022
16:30 Uhr
Prof. Dr. Wolfgang Trutschnig
Paris Lodron Universität Salzburg (Österreich)
Mathematical aspects of copulas and doubly stochastic measures

Zusammenfassung


Copulas and doubly stochastic measures are mostly well known in the statistical community due to Sklar's famous theorem saying that copulas are the link between multivariate distribution functions and their marginals. Copulas, however, exhibit various interesting and surprising mathematical aspects going far beyond statistics. The talk will discuss some of those aspects, in particular some interrelations with functional analysis, geometry, number theory, and fractals.
[Abstract]
[PDF]
vorab Institutstee /-kaffee um 16.00 Uhr im Besprechungsraum M614/616
Mathematikgebäude, Hörsaal E28
Im Rahmen des Mathematischen Kolloquiums
Im Rahmen der Vortragsreihe Angewandte Numerik und Simulation
30.06.2022
15.15 Uhr
Thomas Izgin
Universität Kassel
An Introduction to the Stability of Positivity-Preserving Schemes

Zusammenfassung


Positivity-preserving schemes are of high importance and gained more and more attention in recent years. However, they often result in nonlinear iteration schemes even when applied to a linear test problem y′ = Ay. Hence, a stability analysis becomes more complex. Moreover, the scheme often has to preserve additionally other properties of the analytic solution such as steady states and linear invariants. As a result, steady states of the test problem become non-hyperbolic fixed points of the method. In general, the stability analysis thereby turns into a case by case study.
In this talk, we present sufficient conditions for stability as well as local convergence, and hence, overcome this case by case study for a large class of steady state preserving schemes to which reasonable positivity-preserving schemes belong.
To illustrate the theoretical results, we consider so-called modified Patankar-type schemes that are positive and conservative numerical methods when applied to a positive and conservative production-destruction system. Applying the main theorem we are able to define stability functions which are the basis for the stability analysis. Finally, numerical experiments are presented to confirm the theoretical results.
[Abstract]
[PDF]
M614/616
Im Rahmen des Mathematischen Kolloquiums
11.07.2022
16:30
Prof. Dr. Amin Coja-Oghlan
Fakultät für Informatik, TU Dortmund
Random combinatorial matrices
vorab Institutstee / -kaffee um 16.00 Uhr im Besprechungsraum M614/616
Mathematikgebäude, Hörsaal E28