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WS 2023/24
25.10.2023 um 17:15 Uhr in Raum 69/125
Dr. Samantha Fairchild (Max Planck Institut für Mathematik in den Naturwissenschaften Leipzig)
Lines on a polygon: how hard can it be?
Given a polygon in the plane, consider a point mass moving at unit speed which has perfectly elastic collisions on the boundary. One simple first question is "is there a periodic trajectory?" The answer is yes for all acute triangles and right angled triangles, but remarkably this is still an open problem for most obtuse triangles with an angle at least 112.3 degrees. We will start with a brief discussion of this dynamical system before unfolding to consider polygons called translation surfaces. By working with some concrete examples we will explore some state-of-the art research problems focused on understanding translation surfaces and their associated straight line geodesics.
08.11.2023 um 17:15 Uhr in Raum 69/125
Prof. Dr. Klaus Ritter (RPTU Kaiserslautern-Landau)
Infinite-variate integration and approximation
We consider numerical integration of functions that depend on infinitely many variables. In this talk we focus on general properties of the underlying function spaces and on construction principles for almost optimal quadrature formulas. Moreover, we illustrate that infinite-variate integration naturally arises in the context of stochastic processes with a given series expansion.
22.11.2023 um 17:15 Uhr in Raum 69/125
Prof. Dr. Matthias Reitzner (Universität Osnabrück)
Excess Mortality in Germany 2020-2022
The expected number of all-cause deaths in 2020 to 2022 is computed if there had been no pandemic. This is compared to the number of observed deaths, yielding the excess mortality in Germany for the pandemic years 2020 to 2022. A more detailed analysis yields the excess mortality, resp. mortality deficit for each month and each age group separately. The occurring results are discussed against the number of COVID-19 deaths, pandemic measures, and vaccination rates.
29.11.2023 um 17:15 Uhr in Raum 69/125
Prof. Dr. Nick Vannieuwenhoven (KU Leuven)
Hadamard-Hitchcock decompositions
A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as an elementwise or Hadamard product of several tensor rank decompositions. Such decompositions can encode probability distributions that arise from statistical graphical models associated to complete bipartite graphs with one layer of observed random variables and one layer of hidden ones, usually called restricted Boltzmann machines. We establish generic identifiability of Hadamard-Hitchcock decompositions by exploiting the reshaped Kruskal criterion for tensor rank decompositions. A flexible algorithm leveraging existing decomposition algorithms for tensor rank decomposition is introduced for computing a Hadamard-Hitchcock decomposition. Numerical experiments illustrate its computational performance and numerical accuracy. This is joint work with Alessandro Oneto.
06.12.2023 um 16:15 Uhr in Raum 69/125
Prof. Dr. Giulia Codenotti (Freie Universität Berlin)
Flachheit: Theoreme, Schranken und Werkzeuge
Die Objekte, mit denen wir uns beschäftigen werden, sind konvexe Körper und Polytope (Verallgemeinerungen von Polygonen). Wir interessieren uns dafür, wie sie mit einem Gitter interagieren (man denke an die Punkte mit ganzzahligen Koordinaten). Wir werden das Flachheitstheorem diskutieren, das besagt, dass jedes konvexe Objekt, das keine ganzzahligen Punkte enthält, "flach" sein muss. Wie flach ist aber noch eine offene Frage, und wir werden neuere Werkzeuge vorstellen, die für dieses Problem entwickelt wurden, wie z. B. reduzierte Polytope.
This is an Osnabrücker Maryam Mirzakhani Lecture
20.12.2023 um 17:15 Uhr in Raum 69/125
Prof. Dr. Steffen Sagave (Radboud Universiteit Nijmegen)
Logarithmic ring spectra and their invariants
Commutative rings admit a homotopy theoretic generalization, known as E-infinity rings, and many concepts, constructions, and invariants for rings generalize to E-infinity rings. This provides powerful tools to study topological objects like topological K-theory spectra with algebraic methods, leading to new insights about topology and interesting generalizations of results for ordinary rings. In this talk, I will outline how the concept of logarithmic rings originating from algebraic geometry can be adapted to this homotopical context and discuss examples highlighting why this is useful.
10.01.2024 um 17:15 Uhr in Raum 69/125
Prof. Dr. Stefan Ufer (Ludwig-Maximilians-Universität München)
Logisches Schließen in der Mathematik - Ergebnisse aus Projekten in der Primarstufe und zu Beginn des Mathematikstudiums
Logisches Schließen wird häufig als wesentlicher Teil mathematischen Arbeitens gesehen. Dennoch scheint es zum logischen Schließen mit mathematischen Konzepten lediglich Einzelbefunde zu geben, die meist auf Problembereiche hinweisen. Dagegen weisen Ergebnisse der Entwicklungspsychologie auf frühe Fähigkeiten zum logischen Schließen hin. Der Vortrag gibt einen Überblick über theoretische Beschreibungen logischen Schließens und den Forschungsstand aus der Mathematikdidaktik und der Entwicklungspsychologie. Es werden Ergebnisse aus zwei Projekten berichtet: Anastasia Datsogianni hat in ihrer Promotion das logische Schließen mit Alltagskonzepten und mit mathematischen Konzepten bei Grundschulkindern verglichen. Im Projekt KUM wurde ein Stufenmodell für logisches Schließen zum Beginn des Mathematikstudiums entwickelt. Diskutiert werden Implikationen und offene Fragen, insbesondere zur Rolle von Wissen über die beteiligten mathematischen Konzepte und zur Spezifität von logischem Schließen.
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24.01.2024 um 17:15 Uhr in Raum 69/125
Prof. Dr. Markus Spitzweck (Universität Osnabrück)
Representation categories and motives
Actions of groups reveal symmetries of mathematical objects. In number theory, e.g. representations of Galois groups play an important role. One such example is the action of the absolute Galois group of a number field on the n-torsion points of an elliptic curve or more generally of an abelian variety defined over this field. This instance of etale cohomology motivates modern constructions of categories of motives, which linearize objects from algebraic geometry.
Our aim is to analyze certain parts of such categories by representation theoretic means. We will e.g. formulate universal properties of representation categories of general linear groups (due to Iwanari) and of orthogonal and (general) symplectic groups (which is joint work in progress with Hadrian Heine) over fields of characteristic zero.
31.01.2024 um 17:15 Uhr in Raum 69/125
Prof. Dr. Elisabeth Werner (CWRU Cleveland)
On the Lp Brunn-Minkowski theory
The Brunn Minkowski theory, sometimes also called the theory of mixed volumes, is the very core of convex geometric analysis. It centers around the study of geometric invariants and geometric measures associated with convex bodies. A cornerstone of this theory is the classical Steiner formula.
An extension of the classical Brunn Minkowski theory, the Lp Brunn Minkowski theory has emerged and has evolved rapidly over the last years. It is now a central part of modern convex geometry. The Lp Brunn Minkowski theory focuses on the study of *affine* invariants associated with convex bodies. We show an analogue of the classical Steiner formula in the context of the Lp Brunn Minkowski theory. The classical Steiner formula is a special case of this more general Lp Steiner formula.
