FB 6 Mathematik/Informatik

Institut für Mathematik


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SS 2022

04.05.2022 um 17:15 Uhr in Raum 69/125  TERMIN FÄLLT LEIDER AUS!!!

Prof. Dr. Anna Gusakova (WWU Münster)

Random Simplicial Tessellations: Geometry of the Typical Cell

Abstract

09.05.2022 um 15:00 Uhr s.t. in Raum 69/125       zusätzlicher Termin und neues Thema !

Prof. Dr. Frithjof Lutscher (University of Ottawa, Kanada)

Community dynamics under global change: tipping, tracking, and early
warning signals

Most ecosystems exist in a constantly changing environment. Yet, most models for ecosystem dynamics are based on autonomous dynamical systems and asymptotic analysis of their qualitative behaviour. While seasonality (periodic variation) can still be cast in terms of autonomous systems (by considering the period map), the same is not true for directional variation, such as increasing mean temperatures or increasing habitat destruction and fragmentation. The study of such temporally forced systems is still very much in its infancy. In this talk, I will present some simple population and community models with a linear forcing in one parameter. I will describe the phenomenon of "tracking unstable states", whereby a community can remain near a state that would be unstable, in a temporally constant environment. This phenomenon shows the usefulness and limitations of bifurcation diagrams in the analysis of temporally forced systems. The second focus of my talk will be on early warning signals and the question of whether and how we can predict when a given community might undergo a regime shift, i.e., a large change in state in response to a small change in parameters. 

11.05.2022 um 17:15 Uhr in Raum 69/125

Prof. Dr. Thomas Kahle (Otto von Guericke Universität Magdeburg)

Limit Theorems for Permutation Statistics

It has been long known that the number of descents of a random uniform permutation satisfies a central limit theorem when the size of the permutation group grows. We survey some new limit theorems, where for example, descents are replaced by more interesting statistics, or the permutation group is replaced by a finite Coxeter group, or instead of a central limit theorem, one proves a Gumbel limit of an extreme value statistics.

18.05.2022 um 17:15 Uhr in Raum 69/125

Prof. Akihiro Higashitani, Ph.D. (Osaka University, Japan) 

Introduction to Toric Rings Arising from Combinatorial Objects

One of the main goals in the area of combinatorial commutative algebra is to construct commutative rings from combinatorial objects (e.g., graphs, simplicial complexes, matroids, posets, and so on) and to discuss their algebraic properties in terms of the original combinatorial objects. In this colloquium, I present several typical toric rings arising from combinatorial objects and their algebraic properties. Moreover, we focus on a couple of them and discuss their relationships. 

25.05.2022 um 17:15 Uhr in Raum 69/125

Prof. Dr. Thomas Nikolaus (WWU Münster)

K-Theory and Arithmetic Cohomology Theories

Algebraic K-theory is an invariant of rings. It has several relations to questions in geometric topology, homotopy theory, algebraic geometry and number theory. Recently there have been advances in our understanding how to understand and compute algebraic K-theory using arithmetic cohomology theories.
We will describe sample results, how the relation philosophically works and how it fostered
important advances in p-adic cohomology (notably prismatic cohomology

01.06.2022 um 17:15 Uhr in Raum 69/125

Prof. Dr. Kerstin Tiedemann (Universität Bielefeld)

Vorstellungen zur Multiplikation gemeinsam entwickeln

Grundvorstellungen zur Multiplikation sind normative Kategorien, denen stoffdidaktische Überlegungen zugrunde liegen und die als Orientierung für den Mathematikunterricht in der Grundschule dienen (können). Vor diesem Hintergrund entwickeln Lernende im Unterricht ihre eigenen Vorstellungen zur Multiplikation: Sie begegnen Bildern, Geschichten und Materialien, anhand derer sie Vorstellungen aufbauen sollen, die hinreichend mit den Grundvorstellungen übereinstimmen. Forschungsergebnisse geben Hinweise darauf, dass nicht alle Lernenden dieses Ziel erreichen. Wie kann das sein?

Im Vortrag wird aus einer aktuellen Studie berichtet, in der qualitativ-interpretativ untersucht wird, wie Vorstellungen zur Multiplikation in alltäglichen Unterrichtsgesprächen ausgehandelt werden. Es zeigt sich, dass das Spannungsfeld zwischen Grundvorstellungen und Rechenstrategien größer als gedacht ist und ein wichtiger Ansatzpunkt für die Weiterentwicklung des Unterrichts zum Thema Multiplikation sein könnte.

08.06.2022 um 17:15 Uhr in Raum 69/125

Prof. Dr. Uwe Schmock (Technische Universität Wien)

Modelling and Aggregation of Dependent Risks

The stochastic modelling and aggregation of dependent risks is a central risk management task  for many financial institutions. After an introduction illustrating some basic mathematical challenges, we will review Poisson approximation, the collective model from actuarial science, Panjer distributions, and the extended multivariate Panjer recursion. To assure numerical stability, we introduce weighted convolutions combined with the Panjer recursion, thereby widening the class of mixture distributions. The aim is to discuss a multi-business-line variant of the collective model, mixed by a convex combination of non-negative (mainly unbounded) claim number intensities to obtain an arbitrary linear dependence structure -- and still use recursive methods to calculate the loss distribution of the portfolio. Time permitting, an implementation will be presented, which is available online.

22.06.2022 um 17:15 Uhr in Raum 69/125

Prof. Dr. Michael Cuntz (Leibniz Universität Hannover)

Weyl Groupoids

Reflections and groups generated by reflections appear in many areas of mathematics. For example, crystallographic reflection groups, also called Weyl groups are important invariants attached for example to Lie algebras. The more general Weyl groupoids play a similar role in the theory of quantum groups. Although these Weyl groupoids historically were found in the context of Nichols algebras, they also appear in other situations: they may for example be viewed as toric varieties and in the special case of rank two they correspond to (finite and infinite) frieze patterns and are thus related to cluster algebras.

29.06.2022. um 16:15 Uhr in Raum 69/125

Prof. Dr. Milena Wrobel (Universität Oldenburg)

Torische Varietäten: Eine Brücke zwischen Kombinatorik und Geometrie

Torische Varietäten bilden eine wichtige Test- und Beispielklasse in der algebraischen Geometrie. Der Grund hierfür ist ihre besonders hohe Symmetrie, die es ermöglicht, geometrische Eigenschaften rein kombinatorisch zu beschreiben. Beispielhaft hierfür werden wir im Vortrag das sogenannte Fano-Polytop als kombinatorisches Werkzeug zur Klassifikation von (singulären) torischen Varietäten kennenlernen.
Anschließend betrachten wir den Fall von Toruswirkungen höherer Komplexität, d.h. weniger symmetrischen Varietäten, und zeigen, wie man auch in diesem Fall, zum Beispiel mit Hilfe von Einbettungen in torische Varietäten, kombinatorische Methoden erhält.

This is an Osnabrücker Maryam Mirzakhani Lecture

06.07.2022 um 17:15 Uhr in Raum 69/125

Prof. Dr. Markus Weimar (Ruhr-Universität Bochum)

Rate-Optimal Sparse Approximation of Compact Break-of-Scale Embeddings

In this talk, we shed some light on interrelation of the regularity theory of functions and their approximation properties. We shall discuss general principles that allow to employ the modern theory of function spaces beyond the classical Sobolev-Hilbert scale, in order to quantify the performance of optimal (non-)adaptive algorithms, e.g., for the efficient numerical treatment of elliptic PDEs. Motivated by high-dimensional applications from natural sciences, we will focus on the concept of so-called dominating-mixed smoothness which might help to break the curse of dimensionality. In the course of this, advanced non-linear wavelet-algorithms will be constructed that are able to approximate certain practically relevant embeddings in an asymptotically optimal way. This part of the presentation is based on recent joint work with G. Byrenheid (FSU Jena) and J. Hübner (RUB).