Main content

SS 2024

10.04.2024 um 17:15 Uhr in Raum 69/125

Prof. Dr. Bram Petri (Institut Universitaire de France)

Highly Connected Hyperbolic Surfaces

Hyperbolic surfaces are surfaces equipped with a complete Riemannian metric of constant negative sectional curvature. Equivalently, these are surfaces that are locally isometric to the hyperbolic plane. These surfaces and their moduli spaces appear naturally in many places in mathematics. In this talk I will talk about connectivity questions on hyperbolic surfaces and how probability theory can help approach these questions. This is joint work with Thomas Budzinski and Nicolas Curien. I will not assume any familiarity with hyperbolic geometry.

24.04.2024 um 17:15 Uhr in Raum 69/125

Prof. Dr. Carlos Améndola Cerón(TU Berlin)

Likelihood Geometry of Reflexive Polytopes

We study the problem of maximum likelihood (ML) estimation for statistical models defined by reflexive polytopes. Our focus is on the ML degree of these models as a way of measuring the algebraic complexity of the corresponding optimization problem. We compute the ML degrees of all 4319 classes of three-dimensional reflexive polytopes and prove formulas for several general families, which include the hypercube and the cross-polytope in any dimension. We find some surprising behavior in terms of the gaps between ML degrees and degrees of the associated toric varieties, and we encounter some models of ML degree one. This is joint work with Janike Oldekop.

15.05.2024 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.

22.05.2024 um 16:15 Uhr in Raum 69/125

Prof. Dr. Lisa Sauermann (Universität Bonn)

Über Mengen ohne arithmetische Folgen und verwandte Probleme

Für eine gegebene, sehr grosse positive ganze Zahl N kann man die folgende Frage stellen: Was ist die größtmögliche Größe einer Teilmenge von {1,...,N}, sodass diese Teilmenge keine drei verschiedenen Zahlen x,y,z mit x+z=2y enthält? Also anders gefragt, was ist die größtmögliche Größe einer Teilmenge von {1,...,N}, die keine arithmetische Folge der Länge 3 enthält? Analog kann man für eine gegebene Primzahl p und eine (sehr grosse) positive ganze Zahl n fragen, was die größtmögliche Größe einer Teilmenge des Vektorraums F_p^n über dem endlichen Körper F_p ist, die keine arithmetische Folge der Länge 3 enthält (also, die keine drei verschiedenen Vektoren x,y,z mit x+z=2y enthält). Dies sind grundlegende und seit langem offene Probleme in additiver Kombinatorik. Dieser Vortrag behandelt die bekannten Schranken für diese Probleme und gibt einen Überblick über die dabei verwendeten Beweismethoden sowie über einige weitere Anwendungen dieser Methoden auf andere Probleme in additiver Kombinatorik.

This is an Osnabrücker Maryam Mirzakhani Lecture

05.06.2024 um 17:15 Uhr in Raum 69/125

Prof. Dr. Jochen Heinloth (Universität Duisburg/Essen)

Quotients And Moduli Spaces

A useful trick in geometry is to view the set of all objects of a certain type as a geometric space itself - the moduli space. This sometimes either allows to transport information from particularly symmetric objects to general objects - for example to show that there are exactly 27 lines on each smooth cubic surface - or to distinguish behavior of general and special objects - for example, for each sufficiently general set of 3 circles there are exactly 8 circles simultaneously tangent to each of the three. The existence of degenerate objects, or degenerate configurations, often causes the space of all objects to be ill-behaved. To remedy this, many notions of "stability conditions" have been found, that allow to remove pathological pieces of the space and then obtain nice, compact moduli spaces.

In the talk I want to explain some of these phenomena, starting with examples from linear algebra and then give an idea of more recent results that explain how notions of stability arise from geometry.

12.06.2024 um 17:15 Uhr in Raum 69/125

Prof. Dr. Magdalena Kedziorek (Radboud Universitet Nijmegen)

Interplay Between Commutativity And Symmetry

Homotopy theory that takes symmetries of a space into account, called equivariant homotopy theory, has a long tradition. The foundations of the subject were developed by tom Dieck, Segal, May and their many students and collaborators in the 1960s and 1970s. More recently, equivariant homotopy theory has provided instrumental tools for solving computational and conceptual problems in algebraic topology and algebraic geometry among other parts of mathematics. New developments in the field in the last decades created an incredible amount of activity.

In recent years a lot of attention has been given to the various levels of commutativity in equivariant homotopy theory. Such levels are modelled by N_\infty - operads of Blumberg and Hill. In this talk, I will concentrate on presenting this landscape and outlining how, in some topological cases, it can be described in purely algebraic terms.

19.06.2024 um 16:00 Uhr in Raum 69/125

Priv.-Doz. Mag. Dr. Peter Kritzer (RICAM Linz)

Point Sets With Non-Negative Local Discrepancy And Their Use In Quasi-Monte Carlo Rules

Quasi-Monte Carlo (QMC) rules are equal-weight quadrature rules for approximating integrals of functions depending on many variables. One of the main challenges when studying QMC rules is to find reliable error bounds. In this talk, we present a way of finding a non-asymptotic and computable upper bound for the integral of a function f over [0, 1]^d. Indeed, let f : [0, 1]^d → R be a completely monotone integrand and let points x₀, . . . , x_n−1 ∈ [0, 1]^d have a non-negative local discrepancy (NNLD) everywhere in [0, 1]^d. In such a situation, we can use the points x₀, . . . , x_n−1 in a QMC rule and obtain the desired bound for the integral of f . An analogous non-positive local discrepancy (NPLD) property provides a computable lower bound. We will also discuss which point sets are candidates for having the NNLD or NPLD property. Based on joint work with Michael Gnewuch, Art B. Owen, and Zexin Pan.

26.06.2024 um 17:15 Uhr in Raum 69/125

Prof. Dr. Andreas Focks (Universität Osnabrück)

Using Mathematical And Computer Models To Assess The Environmental Safety Of Chemicals

Chemicals are used by humans in a variety of ways, e.g. as pharmaceuticals, personal care products, household chemicals, biocides, pesticides and industrial chemicals. Chemical residues are ubiquitous in water, soil, air and biota around the world. Negative effects on the survival of species and biodiversity cannot be ruled out. An environmental impact assessment is mandatory before new chemical molecules can enter the market.
In this talk I will show how mathematical and simulation models can support the environmental risk assessment of chemicals, especially pesticides. I will give a brief overview of different methods and illustrate their development using current research projects.