Sommersemester 2026

08.04.2026 um 17:15 Uhr in Raum 69/12

Prof. Martin Frankland, Ph.D (University of Regina, Kanada)

Quillen Cohomology of Divided Power Algebras over an Operad

In topology, cohomology is an invariant we can assign to spaces. In algebra, there are also cohomology theories for various algebraic structures, such as group cohomology, Lie algebra cohomology, and André-Quillen cohomology of commutative rings. Quillen cohomology provides a cohomology theory for any algebraic structure. It has been studied notably for divided power algebras and restricted Lie algebras, both of which are instances of divided power algebras over an operad: the commutative and Lie operad respectively. I will describe joint work with Ioannis Dokas and Sacha Ikonicoff generalizing this to other operads. My main goal will be to introduce the three ingredients in the title.

22.04.2026 um 17:15 Uhr in Raum 69/125

Prof. Dr. Frank Aurzada (Technische Universität Darmstadt)

Brownian Motion – Conditioned on Atypical Events

Brownian motion is a fundamental model in probability theory. In this talk, I will introduce Brownian motion as the limit of simple random walks generated by coin tosses, and then review some of its classical properties. A central theme of the talk is conditioning Brownian motion on events that, in principle, have probability zero. This leads to other interesting stochastic processes. Finally, I will discuss recent results on Brownian motion conditioned not to leave the interval [-1, 1] (for too long). This is joint work with Martin Kolb (Paderborn) and Dominic Schickentanz (Technion).

06.05.2026 um 16:15 Uhr in Raum 69/125

Prof. Dr. Damaris Schindler (Georg-August-Universität Göttingen)

Apollonische Kreispackungen

In diesem Vortrag besprechen wir zahlentheoretische Fragen im Zusammenhang mit Apollonischen Kreispackungen. Nach einer Definition von Apollonischen Kreispackungen, betrachten wir insbesondere die Folge der Krümmungen, die wir in so einer Konstellation sehen. Was können wir über die auftretenden Krümmungen sagen? Welche ganze Zahlen sind Krümmung in einer gegebenen Apollonischen Kreispackung? Um der Frage näher zu kommen, besprechen wir Zusammenhänge mit quadratischen Formen sowie lokal-global Prinzipien. 

This is an    Osnabrücker Maryam Mirzakhani Lecture

13.05.2026 um 17:15 Uhr in Raum 69/125

Prof. Dr. Relinde Jurrius ( Netherlands Defence Academy, Den Haag) 

q-Analogues in Combinatorics 

Roughly speaking, a q-analogue in combinatorics is what happens if we generalize from sets to finite dimensional vector spaces over finite fields. For example, a combinatorial design consists of a finite sets of points, and a family of subsets of this set that all have the same size, such that every pair of points is in exactly one set of this family. For the q-analogue, we start with a finite dimensional vector space, and define a family of subspaces that all have the same dimension, such that every two-dimensional space is in exactly one set of this family. At first sight, this might look like a rather straightforward exercise. And sometimes that is true. But also sometimes q-analogues are very nontrivially, or do not even exist. Furthermore, it can happen that two statements about sets are equivalent, while their q-analogues are not. In this talk we will see many examples and non-examples of q-analogues, and we will dive into linear algebra over finite fields to get some intuition on why q-analogues can be difficult, but also fun.

03.06.2026 um 17:15 Uhr in Raum 69/125

Prof. Dr. Franz Schuster (TU Wien, Österreich)

Radon Transforms of Projection Functions and Aleksandrov-Fenchel Inequalities

The Radon transforms on Grassmannians define a family of geometric maps on convex bodies when applied to their projection functions. These operators coincide on origin-symmetric bodies with the mean section operators introduced in the 1990s by Goodey and Weil and are dual, via the Alesker-Fourier transform, to Minkowski’s family of projection body maps. Over the past two decades various results, including sharp isoperimetric type inequalities, established for projection body maps towards the end of the previous century were shown to also hold for the mean section operators. However, a dual to Lutwak’s family of Brunn-Minkowski type inequalities for the intrinsic volumes of the projection body maps remained open for mean section operators in full generality with several partial results being proved since the early 2000s. In this talk, we present new Alesksandrov–Fenchel inequalities for certain averages of mixed volumes that are the key to show that also all the intrinsic volumes of the Radon transforms of projection functions are indeed log-concave.
(joint work with L. Brauner and O. Ortega-Moreno)
 

17.06.2026 um 17:15 Uhr in Raum 69/125

Prof. Joe Kileel, PhD (University of Texas at Austin, USA)

Low-Rank Tensor Methods in Data Science and Scientific Computing 

Often in data science and scientific computing, high-dimensional data is usefully organized into higher-order arrays.  The higher-order arrays, also known as tensors, may then be factorized through appropriate multilinear decompositions.  This can achieve data compression and/or reveal important latent information. In this talk, I will give an introduction to low-rank tensor methods for a general mathematical audience.  The subject is at the crossroads of linear algebra, optimization, and some geometry. A focus will be on ensuring computational efficiency, despite the curse of dimensionality inherent in tensor methods.  My talk will showcase applications of tensor methods that I have developed, including (time permitting) in computer vision and robotics; mixture modeling in statistics; and the compression of data streams (arising, e.g., from PDE simulations).

24.06.2026 um 16:00 Uhr im Helikoniensaal / Gebäude 64 / Antrittsvorlesung

Prof. Dr. Johanna Schönherr / Prof. Dr. Dr. Johannes Halbe

Titel Schönherr: Wenn Lernende zeichnen: Wie und wann Skizzen das Mathematiklernen unterstützen

Titel Halbe: Transformation mit System: Visionen und Pfade für eine zirkuläre Bioökonomie

08.07.2026 um 16:15 Uhr in Raum 69/125

Prof. Dr. Sabrina Streipert (University of Pittsburgh, USA)

Zwischen Einfachheit und Realismus: Mathematische Modelle motiviert durch Anwendungen in der Fischereiwissenschaft

Mathematische Modelle können wesentlich zum Verständnis von Populationsdynamiken beitragen, etwa in der Fischereiwissenschaft. Bereits einfache mathematische Modelle können dabei wichtige Einsichten liefern und als Frühwarnsysteme für kritische Entwicklungen, etwa im Kontext nachhaltiger Nutzung, dienen. Gleichzeitig stoßen derartige Modelle aufgrund ihrer einfachen Struktur an Grenzen. Beispielsweise berücksichtigen sie keine Altersstruktur. Um dennoch Prozesse wie Entwicklungszeiten oder verzögerte Reproduktion ohne komplexe und datenintensive Modellierung zu erfassen, eignen sich diskrete Verzögerungsmodelle. Der Vortrag zeichnet diesen Weg von einfachen zu strukturierteren Modellen nach und verdeutlicht, wie mathematische Ansätze zum Verständnis grundlegender Mechanismen in Populationssystemen beitragen können.

This is an    Osnabrücker Maryam Mirzakhani Lecture