Talks at the mathematical institute

Michael Kupper:

Risk measures based on weak optimal transport and approximation of drift control problems

Time and place

Friday, 4.4.25, 12:00-13:30, Seminarraum 404

Abstract

We discuss convex risk measures with weak optimal transport penalties and show that these risk measures admit an explicit representation via a nonlinear transform of the loss function. We discuss several examples, including classical optimal transport penalties and martingale constraints. In the second part of the talk, we focus on the composition of related functionals. We consider a stochastic version of the Hopf–Lax formula, where the Hopf–Lax operator is composed with the transition kernel of a Lévy process. We show that, depending on the order of composition, one obtains upper and lower bounds for the value function of a stochastic optimal control problem associated with drift-controlled Lévy dynamics. The value function of the control problem is approximated both from above and below as the number of iterations tends to infinity, and we provide explicit convergence rates for the approximation procedure. The talk is based on joint work with Max Nendel and Alessandro Sgarabottolo.

Moritz Kraßnitzer:

First Order Topological Structures and Theories

Time and place

Tuesday, 22.4.25, 15:00-16:00, Seminarraum 404

Abstract

Max Herwig:

Hrushovskis ab initio Konstruktion

Time and place

Tuesday, 29.4.25, 14:30-16:00, Seminarraum 404

Abstract

Manuel Schlierf:

Gradient flow dynamics for Willmore-type bending energies: global existence, convergence and analysis of singularities

Time and place

Tuesday, 29.4.25, 16:00-17:45, Seminarraum 125

Abstract

Hannes Jakob:

Failure of Approachability at the Successor of the First Singular for any Cofinality

Time and place

Tuesday, 6.5.25, 14:30-16:00, Seminarraum 404

Abstract

Wei Wei:

Geometric inequality related with \(\sigma_2\) curvature

Time and place

Tuesday, 6.5.25, 16:15-17:45, SR 404

Abstract

Jonah Reuß:

A note on the existence of nontrivial zero modes on Riemannian manifolds

Time and place

Tuesday, 13.5.25, 16:15-17:45, Seminarraum 404

Abstract

In this talk we consider nontrivial solutions, so called zero modes, to the Dirac equation on closed Riemannian manifolds. We will state and prove a necessary criterion for the existence of zero modes, which relates the norm of a certain vector field to the Yamabe constant of the manifold. In the end we will give some insight on a classification of manifolds on which this criterion is sharp.

Prof. Dr. Martin GROHE:

The Logic of Graph Neural Networks

Time and place

Thursday, 15.5.25, 15:00-16:30, Hörsaal 2

Abstract

Graph neural networks (GNNs) are deep learning models for graph data that play a key role in machine learning on graphs. A GNN describes a distributed algorithm carrying out local computations at the vertices of the input graph. Typically, the parameters governing this algorithm are acquired through data-driven learning processes.

After introducing the basic model, in this talk, I will focus on the expressiveness of GNNs: which functions on graphs or their vertices can be computed by GNNs? Understanding expressiveness will help us to understand the suitability of GNNs for various application tasks and guide our search for possible extensions.

Surprisingly, the expressiveness of GNNs has a clean and precise characterisation in terms of logic and Boolean circuits, that is, computation models of classical (descriptive) complexity theory.

Robin Riegel:

A Morse theoretical approach to the Chas-Sullivan product

Time and place

Monday, 19.5.25, 16:00-18:00, Seminarraum 404

Abstract

We will discuss how to build (and generalize) a Morse model for a fundamental operation in string topology, the Chas-Sullivan product on the free loop space of a closed manifold. This approach is based on the work of Barraud, Damian, Humilière and Oancea who introduced Morse Homology with differential graded coefficients which they show to be a particularly adapted framework to give a finite dimensional approach to study the homology of total spaces of fibrations over a closed manifold.

Mingwei Zhang:

Dirac-geodesics in surfaces

Time and place

Tuesday, 20.5.25, 16:15-17:45, Seminarraum 404

Abstract

In this talk, we consider the structure of Dirac-geodesics with curvature term in surfaces and give solutions on the 2-sphere and the hyperbolic plane, and then we give the structure of solutions in warped product spaces. Finally, we define the corresponding heat flow and prove the global existence and sub-convergence of the heat flow into any closed surfaces and space forms. This is a joint work with Prof. Q. Chen.

Prof. Dr. Sebastian Wartha:

Operations- und Zahlvorstellungen zu Beginn der Sekundarstufe

Time and place

Tuesday, 20.5.25, 18:30-20:00, Hörsaal 2

Abstract

Spätestens im Zeitalter von KI sei die Frage erlaubt, ob ein „Rechnenkönnen“ – unabhängig von Schulstufen – ein erstrebenswertes Ziel des Mathematikunterrichts sein sollte. Die Suggestivfrage verschärft sich, wenn das Rechnen losgelöst von Grundvorstellungen zu Zahlen und den sie verknüpfenden Operationen geschieht, was aber zahlreiche Studien und Erfahrungen von Lehrkräften berichten. Im Vortrag soll ein Überblick über ausgewählte Kompetenzen von Lernenden in Bezug auf deren Vorstellungen zu Zahlen (natürliche und positiv rationale) und zur Multiplikation mit Ihnen vorgestellt werden. Das ist die Grundlage für konstruktive Vorschläge für unterrichtliche Settings, in denen der Aufbau von Grundvorstellungen sowie die Kommunikation und Argumentation mit und über Zahlen und Operationen im Mittelpunkt steht.

Cagin Ararat:

Systemic Values-at-Risk: Computation and Convergence

Time and place

Monday, 26.5.25, 14:00-15:30, Seminarraum 232

Abstract

We investigate the convergence properties of sample-average approximations (SAA) for set-valued systemic risk measures. We assume that the systemic risk measure is defined using a general aggregation function with some continuity properties and value-at-risk applied as a monetary risk measure. Our focus is on the theoretical convergence of its SAA under Wijsman and Hausdorff topologies for closed sets. After building the general theory, we provide an in-depth study of an important special case where the aggregation function is defined based on the Eisenberg-Noe network model. In this case, we provide mixed-integer programming formulations for calculating the SAA sets via their weighted-sum and norm-minimizing scalarizations. To demonstrate the applicability of our findings, we conduct a comprehensive sensitivity analysis by generating a financial network based on the preferential attachment model and modeling the economic disruptions via a Pareto distribution.

Mingwei Zhang:

Stability of sharp spinorial Sobolev inequality on sphere

Time and place

Tuesday, 27.5.25, 16:15-17:45, Seminarraum 404

Abstract

In this talk we consider the sharp spinorial Sobolev inequality on S^n. From the variation point of view, this is a spinorial analogy of Yamabe problem. It is well known that the optimal Sobolev constant is the so-called Bär-Hijazi-Lott invariant which, as the Yamabe invariant, attains its maximum at round sphere. In this talk, we will prove on S^n that the Sobolev quotient being close to the optimal constant implies that spinor being close to an optimizer. Compared to the function case, the difficulty arises from the fact that the Dirac operator has unbounded spectrum both from above and blow. This is a joint work with Prof. Guofang Wang.

Ludger Overbeck:

Rough and path-dependent affine models and their path-valued interpretation

Time and place

Wednesday, 28.5.25, 16:00-17:30, Seminarraum 226 (HH10)

Abstract

We first extend results on affine Volterra processes to the inhomogeneous case. This includes moment bounds of solutions of Volterra equations driven by a Brownian motion with an inhomogeneous kernel and inhomogeneous drift and diffusion coefficients and in the case of affine drift and variance we show how the conditional Fourier-Laplace functional can be represented by a solution of an inhomogeneous Riccati-Volterra integral equation. For a time homogeneous kernel of convolution type we establish existence of a solution to the stochastic inhomogeneous Volterra equation. If in addition the coefficients are affine, we prove that the conditional Fourier-Laplace functional is exponential-affine in the past path. Finally, we apply these results to an inhomogeneous extension of the rough Heston model used in mathematical finance. Secondly we investigate the equivalence between affine coefficients of a path dependent continuous stochastic differential equations and the affine structure of the log Fourier-transform. Applications in mathematical finance include e.g. delayed Heston model. In both cases the corresponding path processes are infinite-dimensional affine Markov processes. This is joint work (partially in progress) with Julia Ackermann (Wuppertal), Boris Günther (Gießen) und Thomas Kruse (Wuppertal).

Maximilian Stegemeyer:

Resonances of closed geodesics on real projective space and extensions of loop products

Time and place

Monday, 2.6.25, 16:15-17:45, Seminarraum 404

Abstract

Properties of closed geodesics on a Riemannian manifolds are a classical topic of mathematical research. The closed geodesics can be described as the critical points of the energy functional on the free loop space of a manifold. Since string topology studies algebraic structures on the homology of free loop spaces, there is hope that string topology operations give new insights into closed geodesics. In this talk we show one can adapt a result by Hingston and Rademacher for closed geodesics on the sphere to real projective space. Since even-dimensional real projective space are not orientable the classical string topology operations are not defined and some extra care is required. We will show that the loop product and coproduct can be defined on the universal covering space of the free loop space of real projective space and these new operations can be understood as extensions of the loop product and coproduct on the sphere.

Lucas Bouck:

tba

Time and place

Tuesday, 3.6.25, 14:15-15:15, Seminarraum 226, HH10

Abstract

Nelly Harsch:

My internship at Bosch

Time and place

Tuesday, 3.6.25, 15:00-16:30, SR 226 (HH10)

Abstract

Xuwen Zhang:

Bounding the area of submanifolds with prescribed boundary in terms of its curvature energy

Time and place

Tuesday, 3.6.25, 16:15-17:45, Seminarraum 404

Abstract

Given an (m-1)-dimensional, embedded, compact submanifold \(\Gamma\) in \(\mathbb{R}^n\), consider any compact, immersed m-dimensional submanifold whose boundary is exactly given by \(\Gamma\). In this talk, we show how the area of such an m-submanifold is controlled in terms of its curvature energy. The talk is based on joint work with Prof. Ernst Kuwert.

Dr. Julia Sirock:

„Funktionen und Modellieren“ – Einblicke in die Entwicklung eines Inhaltsmoduls aus dem DZLM-Fortbildungsprogramm QuaMath

Time and place

Tuesday, 3.6.25, 18:30-20:00, Hörsaal 2

Abstract

Die Leitidee Funktionaler Zusammenhang spielt nicht nur in vielen Inhaltsbereichen des Mathematikunterrichts eine zentrale und durchgängige Rolle, sondern auch für das Modellieren in vielfältigen Anwendungskontexten. Meist wird dabei das Gelernte auf Situationskontexte übertragen, Anwendungsaufgaben können aber auch gezielt zum Aufbau funktionalen Denkens genutzt werden. Der Vortrag stellt das Modul Funktionen und Modellieren vor, in dem Lehrkräfte sich professionalisieren können, um Verstehensgrundlagen und Modellierungskompetenzen im Bereich des Funktionalen Denkens bei Lernenden aufzubauen, zu diagnostizieren und zu fördern. Neben der Vorstellung von Modulinhalten und Fortbildungsaktivitäten sollen auch erste Einblicke in die Begleitforschung zum Modul gegeben werden.

Bin Deng:

Sharp quantitative estimates of Struwe’s decomposition

Time and place

Thursday, 5.6.25, 14:00-15:00, Seminarraum 125

Abstract

Suppose \(u\in \dot{H}^1(\mathbb{R}^n)\). In a fundamental paper, Struwe proved that if \(u\geq 0\) and \(\|\Delta u+u^{\frac{n+2}{n-2}}\|_{H^{-1}}:=\Gamma(u)\to 0\) then \(dist(u,\mathcal{T})\to 0\), where \(dist(u,\mathcal{T})\) denotes the \(\dot{H}^1(\mathbb{R}^n)\)-distance of \(u\) from the manifold of sums of Talenti bubbles. In this talk, I will talk about a quantitative version of this Struwe’s decomposition. Precisely, we proved nonlinear quantitative estimates for dimension while Figalli-Glaudo proved a linear estimate for dimension . Furthermore, we showed that these estimates are sharp in the sense of the exponents are optimal. It is joint work with Liming Sun and Juncheng Wei.

Bao Yu:

Liouville type theorem for a class quasi-linear \(p\)-Laplace equation on the half space

Time and place

Thursday, 5.6.25, 15:00-16:00, Seminarraum 125

Abstract

In this talk, we will study the positive solutions of p-Laplacian with subcrtical exponent in the half space with the Neumann boundary condition. We deduce a Liouville Theorem via the method of vector field and integral by part motivated by Obata. This is a joint work with Xinan Ma and Yang Zhou.

Bora Yalkinoglu :

On arithmetic properties of discrete Toda flows

Time and place

Friday, 6.6.25, 10:30-11:30, Seminarraum 404

Abstract

We will explain a new linearization of the discrete periodic Toda flow (a well known discrete integrable system) in terms of Mumford's description (via quadratic forms and Gauß composition law) of Jacobians of hyperelliptic curves. A subtle integrality property appearing in this set-up opens the way to use p-adic methods for the study of the Toda flow. We will give an elementary talk explaining all the main actors and also point to some intriguing connections with number theory.

Catharina Stroppel :

A braided monoidal 2-category via Soergel bimodules

Time and place

Monday, 16.6.25, 14:15-15:15, Seminarraum 232

Abstract

Braided monoidal categories are good sources for topological invariants. To get more refined invariants, or even a full TQFT, one might want to lift this a categorical level higher and construct a braided monoidal 2-category. The talk will start by reviewing some well-known facts with an important example of a braided monoidal category. Then I will try to explain why the construction of a braided monoidal 2-category, and even the definition of such an object, is not obvious. The second part of the talk will then indicate an actual construction using complexes of Soergel bimodules.

Eric Trébuchon:

Regularity of the Dirac Operator on corner domains

Time and place

Monday, 16.6.25, 16:15-17:45, Seminarraum 404

Abstract

This talk addresses the Dirac operator on polygonal domains in \(\mathbb{R}^2\) with local boundary conditions. While the theory is well-developed for smooth boundaries, much less is known in the presence of corners. We establish symmetry and regularity of the Dirac operator under these generalized conditions. Initial progress toward proving self-adjointness will also be discussed, including an explicit description of the adjoint operator and its decomposition into regular and singular components at the corners. These results provide a foundation for further study of spectral and boundary value problems for Dirac operators on non-smooth domains. The results are based on my own research.

Florian Johne:

TBA

Time and place

Tuesday, 17.6.25, 16:15-17:45, Seminarraum 125

Abstract

Giuseppe Ancona:

Ramified periods and field of definition

Time and place

Friday, 20.6.25, 10:30-12:00, Seminarraum 404

Abstract

In a joint work with Dragos Fratila and Alberto Vezzani, we construct hyperelliptic curves of large genus, defined over quadratic fields that are isomorphic to their Galois conjugates but do not descend to Q. The obstruction to descent is new and we call it “ramified periods”. These are p-adic numbers that arise from the comparison between de Rham cohomology and crystalline cohomology (hence the term periods). These numbers can reveal interesting information if p ramifies in the quadratic field.

Thorsten Hertl:

t.b.a.

Time and place

Monday, 23.6.25, 16:00-17:30, Seminarraum 404

Abstract

Linn Hansen :

Unterrichtsqualität verstehen: Die Entwicklung und der Einsatz kontrastierender Praxisrepräsentationen in der Lehrkräftebildung am Beispiel des Mathematikunterrichts

Time and place

Tuesday, 24.6.25, 18:30-20:00, Hörsaal 2

Abstract

Um die Unterrichtsqualität an Schulen zu verbessern, sollten (angehende) Lehrkräfte frühzeitig die Möglichkeit erhalten, Wissen über Unterrichtsqualitätsmerkmale zu erwerben. Da diese Merkmale oft schwer direkt zu beobachten sind, können gezielt entwickelte Praxisrepräsentationen dabei helfen, sie sichtbar zu machen. Im Vortrag wird daher ein systematischer Ansatz zur Entwicklung solcher Praxisrepräsentationen in Form von geskripteten Videos vorgestellt. Die Kombination von Erkenntnissen aus der Entwicklung von Videovignetten und der Variationstheorie ermöglicht es, typische Unterrichtspraktiken und deren Auswirkungen auf Unterrichtsqualitätsmerkmale praxisnah und kontrastierend darzustellen. Der Vortrag gibt einen Überblick über die Einsatzmöglichkeiten der entwickelten Unterrichtsvideos sowohl in der Lehrkräftebildung als auch in der Forschung, die Fragen zur Fachspezifität von Unterrichtsqualitätsratings untersucht.

Prof. Dr. Damien Gayet:

What does a random complex curve look like locally?

Time and place

Thursday, 26.6.25, 15:00-16:30, Hörsaal 2

Abstract

A complex curve of degree d in the complex projective plane is the vanishing locus of a homogeneous polynomial of degree d. These curves are real surfaces satisfying a spectacular collective feature: generically they are all topologically the same, that is connected compact Riemann surfaces with genus equal to (d-1)(d-2)/2. Now, if we fix a ball and we look at the intersection of the curve with this ball, this magical property disappears completely. For instance, the curve can simply miss the ball. But if the polynomial is chosen at random and has a high degree, we can expect intuitively that the ball will capture, in average, a fixed proportion of the global topology of the curve. I will explain that this is the case.

Guofang Wang:

TBA

Time and place

Tuesday, 1.7.25, 16:15-17:45, Seminarraum 125

Abstract

Prof. Dr. Barbara Niethammer:

Free boundary problems in models for cell polarization

Time and place

Thursday, 3.7.25, 15:00-16:30, Hörsaal 2

Abstract

Cell polarization denotes the rearrangement of certain substances on the membrane of a cell in response to an external chemical signal. It is a crucial ingredient in many biological processes, such as for example the motion of cells. Starting from a bulk-surface reaction-diffusion system for several protein densities describing this process, we rigorously derive nonlocal free boundary problems that allow for a relatively simple characterization of polarization. For these limit systems we prove global stability of steady states and characterize the parameter regime for the onset of polarization. We also discuss some aspects of regularity in time of the free boundary.

(joint work with A. Logioti (Stuttgart), M. Röger (Dortmund) and J. Velazquez (Bonn))

Simon Ebert:

tba

Time and place

Monday, 7.7.25, 16:15-17:45, Seminarraum 404

Abstract

Xuwen Zhang:

TBA

Time and place

Tuesday, 8.7.25, 16:15-17:45, Seminarraum 404

Abstract

Valerie Freund:

t.b.a.

Time and place

Monday, 14.7.25, 16:15-17:45, Seminarraum 404

Abstract

Florian Johne:

TBA

Time and place

Tuesday, 15.7.25, 16:15-17:45, Seminarraum 125

Abstract

Dr. Michael Bürker :

„Die Mathematik ist die Sprache der Natur“ – Spannende Aufgaben mit historischem Hintergrund

Time and place

Tuesday, 15.7.25, 18:30-20:00, Hörsaal 2

Abstract

In der Auseinandersetzung mit historischen Problemen der Mathematik können Schülerinnen und Schüler die Wirkungskraft mathematischer Argumentationen erfahren: Welche Argumente haben Mathematikerinnen und Mathematiker früherer Zeit genutzt, denen unsere technischen Hilfsmittel nicht zur Verfügung standen? Wie konnten beispielsweise die Zeitgenossen von Euklid den Erdumfang und die Entfernung zum Mond bestimmen? Im Vortrag werden einige spannende Aufgaben mit historischem Hintergrund vorgestellt. Dabei geht der Referent auf die Frage ein, an welchen Stellen Verständnisschwierigkeiten zu erwarten sind und welche Hilfe man den Lernenden anbieten könnte. Bei den im 20. Jahrhundert vieldiskutierten „unanschaulichen“ Effekten der Speziellen Relativitätstheorie wird im Vortrag gezeigt, wie die durch reine Logik geprägte Argumentation mit Mitteln der Schulmathematik veranschaulicht werden kann.

Benjamin Brotz:

tba

Time and place

Monday, 28.7.25, 16:15-17:45, Seminarraum 404

Abstract