Wintersemester 2025/26:

27.11. Dr. Peter Gorzolla (Frankfurt)
Prozessbegleitung statt Plagiatsjagd. Umgang mit KI in Studium und Lehre am Beispiel der KI-Strategie des Historischen Seminars Frankfurt

Abstract:

Der ChatGPT-Schock an den Universitäten hat ganz früh schon die Fächer getroffen, in denen das wissenschaftliche Schreiben eine zentrale Rolle spielt. Auf der Suche nach einem pragmatischen Weg zwischen Weltuntergangsszenarien und Kopf-in-den-Sand-stecken, der zugleich die eigenen wissenschaftlichen Grundsätze nicht verrät, hat das Historische Seminar im Dezember 2024 als erstes Institut an der Goethe-Universität eine KI-Strategie für Studium und Lehre verabschiedet. Inzwischen ist diese als Diskussionsgrundlage und Konzeptvorlage bei verschiedenen anderen Fächern der Goethe-Universität verbreitet.

11.12. Prof.Dr. Michael Wand (Mainz)
Deep Learning, Generative Models, Transformers & LLMs — A Short Tour of the Basics

Abstract:

In this talk, I will try to provide a quick birds-eye overview of the technical and conceptual background of current AI-models. I will start with a brief recap of machine learning as such, including a discussion of fundamental impossibility results (no-free-lunch, bias-variance trade-off). Afterwards, I will provide a short introduction into how deep learning works, and why it is rather surprising that it works so well. Finally, I will sketch some of the technical steps involved in building a modern „generative“ model that learns data distribution of text, images or other modalities. The main message of the talk will be that the technical steps involved are rather mundane but the fact that this is sufficient to create strongly generalizing statistical models is actually remarkable and rather counter-intuitive.

18.12. Prof.Dr. Wolfgang Soergel (Freiburg)
Kazhdan-Lusztig-Theorie

Abstract:

Die Untersuchung stetiger Operationen von Gruppen wie GL(n;R) und GL(n;C) auf Banachräumen führt zu interessanten algebraischen Fragestellungen. Auf diesem Gebiet sind in jüngerer Zeit große Fortschritte erzielt worden, und darüber will ich berichten.

15.1.: Festkolloquium anlässlich der Verabschiedung von Dr. Cynthia Hog-Angeloni
Prof. Dr. Stephan Rosebrock (Karlsruhe)
Labelled Oriented Trees and the Whitehead Conjecture

Abstract:
The Whitehead conjecture asks whether a subcomplex of an aspherical 2-complex is always aspherical. This question has been open since 1941. Howie has shown that the existence of a finite counterexample implies (up to the Andrews-Curtis conjecture) the existence of a counterexample within the class of labelled oriented trees. Labelled oriented trees are algebraic generalisations of Wirtinger presentations of knot groups. In this talk we start with an introduction into the field. Then we present several possibilities to show asphericity within the class of labelled oriented trees. There are many known classes of aspherical LOTs given by the weight test of Gersten, the I-test of Barmak/Minian, LOTs of Diameter 3 (Howie), LOTs of complexity two (Rosebrock), injective LOTs (Harlander/Rosebrock) and several more. We will present some of these.

22.1. Prof.Dr. Rainer Kaenders (Bonn) muss wegen Erkrankung des Vortragenden leider ausfallen!
Der Lehramtsstudiengang in Bonn mit einer von Otto Toeplitz inspirierten genetischen Einführung in die Infinitesimalrechnung

Abstract:
Seit dem WS 2017/18 haben wir in der Mathematiklehrerbildung der Universität Bonn eine einjährige Veranstaltung „Grundzüge der Mathematik“ für Lehramtsstudierende etabliert, die im Wintersemester mit 11 ECTS aus einer inhaltlichen Vorlesung „Grundzüge der Mathematik I“ (4 SWS) mit Übungen (2 SWS) und einer zusätzlichen Hörsaalveranstaltung (2 SWS) „Rechen- und Argumentationstechniken“ und dazu nochmal Übungen besteht (2SWS). Im Sommersemester gibt es bei den „Grundzügen der Mathematik II“ (6 ECTS) weiterhin die Vorlesung (2 SWS) mit Übungen (2 SWS). Zusätzlich kommt mit 9 ECTS die Vorlesung „Lineare Algebra“ (4 SWS) mit Übungen (2 SWS) hinzu. Im zweiten Jahr folgt dann die Analysis I, die gemeinsam mit den Erstsemestern des Mathematik Bachelors gehört wird.
Der Vortrag stellt die Bonner Mathematiklehrerbildung dar und befasst sich mit der inhaltlichen Konzeption der „Grundzüge der Mathematik“.

5.2. Prof. Dr. Alberto Cogliati (Padova Univ) muss wegen Erkrankung des Vortragenden leider ausfallen!
On the History of Gauss’s Theorema Egregium

Abstract:

The publication of Disquisitiones circa superficies curvas (1828) is widely regarded as marking the beginning of modern differential geometry. Although important results in the geometry of curves and surfaces had already been achieved during the 18th century, Gauss’s contribution inaugurated an entirely new phase in the development of the discipline. The composition of the Disquisitiones was the result of a long process of reflection and successive revisions that occupied Gauss—albeit intermittently—for well over a decade. Despite its brevity, the work stands out for the careful choice of the techniques employed and the meticulous care in which they are presented. My contribution aims to explore the intellectual journey that led Gauss to the final drafting of this work, with particular attention to the discovery of the Theorema Egregium.

15.05. Prof. Dr. Henrik Garde (Aarhus Univ.)
Reconstruction of inclusions and cracks in Calderón’s inverse conductivity problem

Abstract:

The inverse conductivity problem (called Calderón’s probblem), is to determine the interior electrical conductivity from boundary electrical measurements, in practice using electrodes placed on the surface of an object, or on the skin of a person.

I will talk about the exact reconstruction of general inclusions in Calderón’s problem from local boundary measurements. Here „inclusion“ means the support of perturbations to a known reference conductivity.

I will briefly outline the cases on open sets, without going into too much analysis. The perturbed coefficient can have finite positive and negative perturbations, can have perfectly conducting parts and have perfectly insulating parts, and may also have parts given as restrictions of Muckenhoupt coefficients with singular and degenerate behavior (enabling continuous growth to infinity or decay to zero).

I will give a more detailed account of newer results, on reconstructing general cracks given as unions of Lipschitz hypersurfaces, including both perfectly conducting and perfectly insulating cracks.

Finally, if time permits it, I will give results on how practical electrode models are rigorously included, and with application to actual measurements from a physics lab.

12.06. Prof.Dr. Laurent Mazliak (Sorbonne)
Émile Borel and the probabilistic turn of a worried Cantorian

Abstract: In this talk, I shall present the singular way in which Émile Borel, from his studies on the structure of real numbers and certain rejection of Cantor’s abstract vision, found in the calculus of probabilities an adequate tool to formulate a new approach to problems. At the same time, he became aware of the usefulness of the approach to the phenomena of physics and society and developed a singular approach to the problem of interpretation of the concept of probability, merging subjectivist and objectivist aspects under an idiosyncratic formulation of the so-called Cournot principle.

03.07. Prof. Dr. Tobias Dyckerhoff (Univ. Hamburg)
Geometric perspectives on categorical braid group actions

Abstract: One of the many intriguing discoveries inspired by Kontsevich’s homological mirror symmetry is the concept of spherical twists, introduced by Seidel and Thomas. These are autoequivalences described by a categorification of the classical Picard-Lefschetz formula for monodromy actions on homology. More recently, it was proposed by Kapranov and Schechtman to interpret spherical twists within a (still hypothetical) theory of categorical analogs of perverse sheaves, so-called perverse schobers. In this talk, I will give an introduction to this circle of ideas, outline some recent progress on perverse schobers, and explain how they provide new structural insights on categorical braid group actions relevant for link homology theory.

17.07. Prof. Dr. Amru Hussein (Universität Kassel)
Title: From old make new – coupling of partial differential equations

Abstract: Partial differential equations help us to express physical principals and to describe problems in engineering. Once there is more than a single influence, we have to take care of the possible interactions. From a mathematical point of view one can ask which of these are admissible and therefore allows one to make from an „old“ well-understood uncoupled setting a „new“ one – now coupled and interconnected. This is exemplified for coupling boundary conditions on networks where information can be transmitted in various ways through the nodes, and for interconnected systems in fluid mechanics. Examples of the latter are geophysical flow equations describing the dynamics of ocean and atmosphere, and models describing liquid crystals which entered our every day life as liquid crystal displays or LCDs.

24.10. Prof. Dr. Alicia Dickenstein (Buenos Aires)
Algebraic Geometry Tools in Systems Biology

Abstract: In recent years, methods and concepts of algebraic geometry, particularly those of real and computational algebraic geometry, have been used in many applied domains. In this talk, aimed at a broad audience, I will review applications to molecular biology. The goal is to analyze standard models in systems biology to predict dynamic behavior in regions of parameter space without the need for simulations. I will also mention some challenges in the field of real algebraic geometry that arise from these applications.

21.11. Festkolloquium anlässlich des 90. Geburtstages von Prof. Dr. Albrecht Pfister
Sprecher:
16:45h: Prof. Dr. Claus Scheiderer (Uni Konstanz):
Hilberts 3-Quadrate-Satz für ternäre Quartiken: ein elementarer Beweis

Zusammenfassung: Im Jahr 1888 veröffentlichte Hilbert eine fundamentale Arbeit über Quadratsummen reeller Polynome, die großen Einfluß auf zukünftige Entwicklungen nehmen würde. Eines der Hauptergebnisse besagt, daß jede nichtnegative ternäre Form vom Grad vier als Summe von drei Quadraten quadratischer Formen geschrieben werden kann. Hilberts Beweis verwendete subtile Argumente aus Topologie und algebraischer Geometrie, die seiner Zeit teilweise weit voraus waren. In den frühen 2000er Jahren wuchs bei Pfister die Überzeugung, daß Hilberts Satz auch mit elementaren Techniken beweisbar sein sollte. In gemeinsamer Arbeit mit dem Sprecher wurde ein solcher Beweis in den Folgejahren gefunden und wurde 2012 publiziert. In meinem Vortrag werde ich diesen Zugang skizzieren, und werde auch erklären, inwiefern weitere Arbeit von Pfister in den letzten Jahren noch zu einer Verbesserung geführt hat.

17:45h: Prof. Dr. Detlev Hoffmann (TU Dortmund):
Das quadratische Zariski-Problem

Zusammenfassung: Pfisters Arbeiten über quadratische Formen aus den 1960er Jahren, insbesondere der sogenannte Cassels-Pfister-Teilformensatz, können als Ausgangspunkt der Theorie der Funktionenkörper von Quadriken angesehen werden, die dann von Knebusch in den 1970er Jahren systematisch ausgebaut wurde und durch neue algebraisch-geometrische Methoden, die auf Voevodsky und Rost in den 1990ern zurückgehen, eine enorme Weiterentwicklung erfuhr. In diesem Vortrag wollen wir ein noch ungelöstes Problem aus diesem Themenkreis vorstellen: das quadratische Zariski Problem, in welchem die Frage gestellt wird, ob zwei stabil birational äquivalente Quadriken gleicher Dimension schon birational äquivalent
sind. Wir geben eine weitestgehend elementare Einführung in die Fragestellung und präsentieren einige aktuelle Ergebnisse.

09.01.Prof. Dr. Jaap Top (Groningen):
The Bas/Serra surface(s)

Abstract: Many of the enormous abstract sculptures by the recently deceased American „postminimalist“ artist  Richard Serra have a German connection: the Pickhan company in Siegen fabricated them 20-30 years ago. Mathematician Bas Edixhoven recognized a geometrical interpretation of one of them. This resulted in a place for Bas among the artists with artworks on display in the Virtual Museum Tesseract.
The present talk, originally intended in memory of Bas Edixhoven,  aims to recall and explain  these contributions by Bas, and place it in a more general framework of inspirations from Math to Art and, as in this case, vice versa.

23.01. Prof. Dr. Christian Krattenthaler (Wien):
Proofs of Borwein Conjectures

Abstract: The (so-called) „Borwein Conjecture“ arose around 1990 and states that the coefficients in the polynomial (1-q)(1-q^2)(1-q^4)(1-q^5)\…(1-q^{3n-2})(1-q^{3n-1}) have the sign pattern +–+–\….
This innocent looking prediction has withstood all proof attempts until three years ago when Chen Wang found a proof that combines asymptotic estimates with a computer verification for „small“ n.
However, Borwein made actually in total three sign pattern conjectures of similar character – with the previously mentioned conjecture being just the first one -, and recently Wang discovered a further one.
It seemed unlikely that Wang’s proof could be adapted to work for these other conjectures since it crucially used identities that are only available for the „First Borwein Conjecture“.
I shall start by presenting these conjectures and then review the history of the conjectures and the various attempts that have been made to prove them – as a matter of fact, these attempts concerned exclusively the „First Borwein Conjecture“, while nobody had any idea how to attack the other conjectures.
I shall then outline a proof plan that is (in principle) applicable to all these conjectures. Indeed, this leads to a new proof of the „First Borwein Conjecture“, the first proof of the „Second Borwein Conjecture“, and to a proof of „two thirds“ of Wang’s conjecture.
We are convinced that further work along these lines will lead to – at least – a partial proof of the „Third Borwein Conjecture“.
I shall close with further open problems in the same spirit. This is joint work with Chen Wang.

06.02. um 15:30 Uhr „Aufbruch zu neuen Aufgabenfeldern“
Verabschiedung von Prof. Dr. Duco van Straten

19.04. (12 Uhr) Vasily Golyshev (ICTP Trieste):
Lifting differential equations, in-dept

Abstract: I will introduce generalized Heun’s equations following Boalch-Katz-Simpson,
and show how two equations in BKS correspondence share the same kernell.
This is joint work in progress with Ilia Gaiur.

2.5.   Antrittsvorlesung  (16:00 h, Audimax)
Prof. Dr. Hendrik Ranocha (Mainz):
Numerische Mathematik

16.5. Prof. Dr. Matthias Lesch (Univ. Bonn):
The product formula for Fredholm determinants and related questions

Abstract: Fredholm determinants are the natural generalization of Linear Algebra determinants to certain operators acting on a Hilbert or Banach space being naturally related to the trace resp. trace ideals (e.g. B.Simon’s Book on trace ideals). Its product  formula (for operators of the form I+A with A in a higher trace ideal) has only quite recently be fully understood and it exhibits quite some interesting combinatorial features. I will report on a proof  which was developed in a recent Masters Thesis with my student  Nikolaos Koutsonikos-Kouloumpis (https://arxiv.org/abs/2202.12923).  If time permits I will hint at another a priori quite different generalization of determinant in the context of elliptic operators; a posteriori there are interesting relations between the two notions. That latter is joint work with Luiz Hartmann (J. Funct. Anal. 283 (2022))

13.6. Prof. Dr. Frank den Hollander (Univ. Leiden):
The Friendship Paradox for Social Networks

Abstract: In 1991, the American sociologist Scott Feld discovered the paradoxical phenomenon that `your friends are more popular than you are‘. This statement means the following. Consider a group of individuals who form a social network. For each individual in the group, compute the difference between the average number of friends of friends and the number of friends (all friendships are mutual), and average these numbers over all the individuals in the group. It turns out that the latter average is always non-negative, and is strictly positive as soon as not all individuals have exactly the same number of friends. This bias, which at first glance seems counterintuitive, goes under the name of friendship paradox, even though it is a hard fact. In this lecture we model the social network as a sparse random graph. We explain where the bias comes from, how it can be quantified, and illustrate our findings with two examples.
Based on joint work with R.S. Hazra and A. Parvaneh.

20.6. Prof. Dr. Jochen Schütz (Hasselt University):
A class of parallel-in-time multi-derivative time integrators

Abstract: In this talk, we present a class of parallel-in-time multi-derivative time integrators for ordinary (and partial) differential equations. The distinguishing feature of multi-derivative schemes is that they do not only use the information on the time derivative u_t of the unknown solution u (in an ODE, this information could be u_t = f(u)), but also information on higher-order time derivatives u_tt (in the example, u_tt = f'(u) f(u)), u_ttt and so on. We show how this can in practice be used to generate high-order, parallel-in-time schemes that are suitable to integrate highly stiff equations in time. A focus is set on stability of these methods, both classical linear stability as well as asymptotic stability in the stiff limit are treated.

11.7. Prof. Dr. Peter Ullrich (Univ. Koblenz):
Von Euler über Dirichlet zur Riemannschen Zeta-Funktion

Abstract: Die Zeta-Reihe, die die nach Bernhard Riemann (1826–1866) benannte Zeta-Funktion definiert, wurde bereits von Leonhard Euler (1707–1783) untersucht: Zum einen bestimmte er deren Werte für gerade natürliche Argumente, zum anderen gab er die nach ihm benannte Produktdarstellung für sie an.
Beide Ergebnisse publizierte er auch in Lehrbüchern.
Auf die Herleitung der Produktdarstellung in der Introductio in analysin infinitorum nahm Gustav Lejeune Dirichlet (1805–1859) im Jahr 1837 bei seinem Beweis des Primzahlsatzes für arithmetische Progressionen expliziten Bezug. Weiterhin gab er von seinem Wissen über die mathematischen Schriften Eulers an Riemann weiter, der 1859 in seiner Arbeit „Über die Anzahl der Primzahlen unter einer gegebenen Größe“ ebenfalls auf die Produktdarstellung verwies.
Im Vortrag wird analysiert, wie die genannten Ergebnisse zur Entstehung der analytischen Zahlentheorie beigetragen haben.

Freitag, 27.10., 15:30-18:00h!
Festkolloquium Stephan Klaus:

Prof. Dr. Peter Teichner (MPI Bonn)
Eine Vorlesung à la Stephan Klaus

Abstract: Wir erklären einen elementaren Zugang [Dold-Thom] zu Homologie in Termen von Konfigurations-Räumen von geladenen Partikeln. Viele Eigenschaften von Homologie, wie das Mayer-Vietoris-Prinzip, haben sehr intuitive Beweise, das Cup-Produkt ist ganz einfach.
Wege in einem dieser Konfigurations-Räume sind Feynman-Graphen und in der Tat gibt es einen direkten Zusammenhang zur mathematischen Theorie von Quanten-Observablen in Termen von Faktorisierungs-Algebren [Costello-Gwilliam].
Am Ende der Vorlesung steht ein weiterer Zusammenhang, diesmal zu verallgemeinerten Homologie-Theorien (Konfigurations-Räume liefern übliche Homologie mit Werten in der abelschen Gruppe der Ladungen) und dem Goodwillie-Kalkül von analytischen Funktoren.

Prof. Dr. Wilderich Tuschmann (KIT):
Räume und Modulräume Riemannscher Metriken

Abstract: Auf jeder differenzierbaren Mannigfaltigkeit gibt es Riemannsche Metriken, doch die Existenz beziehungsweise Konstruktion von Metriken mit bestimmten vorgegebenen Eigenschaften wie zum Beispiel Nichtnegativität oder auch Negativität der Schnittkrümmung, Positivität der Skalar- oder Ricci-Krümmung, Erfüllung von Einstein-, Kähler- oder anderen speziellen Holonomie-Bedingungen, etc., auf offenen oder geschlossenen glatten Mannigfaltigkeiten stellen seit jeher fundamentale Frage- und Aufgabenstellungen der Globalen Differentialgeometrie dar. Sind diese gelöst, so schließt sich daran direkt eine in der aktuellen Forschung ebenso wichtige Frage an:
’Wie viele’ verschiedene Metriken eines solchen Typs gibt es als Ganzes auf der zugrundeliegenden Mannigfaltigkeit, und ’wie viele’ dadurch definierte verschiedene solcher Geometrien lässt sie überhaupt zu?
In meinem Vortrag werde ich eine elementare Einführung in diese Thematik, zu der speziell auch Professor Klaus gearbeitet hat, sowie einen näheren Über- wie Einblick in grundsätzliche Resultate und offene Fragen auf diesem Gebiet geben.

9.11. Prof. Dr. Calvin Tadmon (Dschang):
Health and environment friendly committed Mathematics:
A model of the immune response to hepatitis B virus infection

Abstract: This talk is about using mathematics for contributing to the improvement of health and protection of the environment. Our focus is on formulating and analysing partial differential equations models for describing and deeply understanding the dynamics of infectious diseases. We first present the general setting of the problem and mention some mathematical methods for analysing it. Then we apply part of the aforementioned methodology to propose and investigate a model of the immune response to hepatitis B virus infection. We also list some of our other significant contributions in the field of mathematical epidemiology. Finally, we envisage skillful incorporation of some relevant environmental drivers, including climate change, and aim at investigating their influence on the evolution of some infectious diseases.

16.11. Prof. Dr. Alina Chertock (North Carolina SU)
Asymptotic Preserving Numerical Methods for Multiscale Problems

Abstract: Many phenomena in nature exhibit multiscale behaviors, which can be rather different in character. These phenomena can be categorized into two groups. On the one hand, there are problems featuring localized singularities, such as boundary or internal layers, shocks, and dislocations. On the other hand, there are problems, such as porous media flows, turbulent flows, and highly oscillating models, where microscopic and macroscopic scales coexist across the entire domain.
When several scales occur in a physical problem, using an approach that describes the phenomenon on a single scale is insufficient. Describing the problem at a microscopic level offers exceptional physical accuracy but is computationally impractical. Likewise, adopting a macroscopic description, where explicit equations for the macroscopic scale are used, effectively eliminating the other scales, is also unsuitable. As such, a multi-scale modeling strategy becomes essential. This involves employing different models to describe phenomena at various scales while balancing the trade-off between numerical accuracy and computational efficiency. The primary objective of multi-scale techniques is to develop numerical schemes that bridge the microscopic and macroscopic scales, outperforming the computational demands of solving the complete microscopic model while still delivering the desired level of accuracy.
Among many other approaches, a special class of numerical methods, known as Asymptotic Preserving (AP) schemes, was developed specifically for multiscale problems. The fundamental concept involves designing numerical techniques that maintain the asymptotic behavior across the transition from microscopic to macroscopic models within a discrete framework. Consequently, AP schemes seamlessly bridge the two scales: the transition between the two scales is implemented effortlessly in that a micro solver automatically becomes a macro solver if the numerical discretizations fail to resolve the physically small scales. As a result, the AP methodology offers straightforward, robust, and efficient computational tools for a wide array of multiscale problems, including kinetic, hyperbolic, and other physical problems. This talk provides an overview of the core concept, design principles, and several representable AP schemes.

30.11. Antrittsvorlesungen (Konferenzraum des Helmholtz Instituts):
16:ooh:
Prof. Dr. Georg Tamme (Mainz)
Algebraische K-Theorie
17:00h
Prof. Dr. Tom Bachmann (Mainz)
Motivische Topologie

11.1. Prof. Dr. Stephan Berendonk (Wuppertal):
Von drei Lernumgebungen zur Elementargeometrie

Abstract: Kongruenzsätze, Strahlensätze, Winkelsumme im Dreieck, Pythagoras und Thales. Schon mit diesem überschaubaren schulgeometrischen Erfahrungsschatz lässt sich in der Elementargeometrie kreativ und forschend tätig sein. Im Vortrag werden drei elementargeometrische Lernumgebungen vorgestellt, anhand derer verschiedene Aspekte des Betreibens von Mathematik erfahren werden können. Bei der ersten Lernumgebung geht es um einen Wettstreit der Konstruktionen, genauer der klassischen Konstruktionen mit Zirkel und Lineal. Die zweite Lernumgebung handelt von einer Art ‚Imitation Game‘, bei dem wir versuchen klassische Beweise des pythagoreischen Lehrsatzes im Falle nicht-rechtwinkliger Dreiecke weitestgehend zu imitieren, in der Hoffnung, dabei Beweise für den Kosinussatz zu erhalten. In der dritten Lernumgebung gilt es nach dem Vorbild des Pantographen, der eine zentrische Streckung verkörpert, weitere geometrische Abbildungen durch geeignete Stangenkonstruktionen zu realisieren. Alle drei Lernumgebungen haben einen spielerischen Charakter und zielen auf ein entsprechendes Bild von Mathematik als Tätigkeit ab.

TERMINVERSCHIEBUNG auf 8.2.
Prof. Dr. William Brewer (FU Berlin):
Kurt Gödel – An exceptional mathematician and an exceptional human being

Abstract: Kurt Gödel is considered by many to be ‘the most important logician of the 20th century’. Nevertheless, he is not well known outside professional logic and philosophical circles. In this talk, we start with a brief summary of his life and career, then consider in more detail his most important achievements in logic/fundamentals of mathematics and set theory, his early visits to the IAS/Princeton, and his lesser-known contributions to philosophy, cosmology, and computer science, as well as his friendship with Albert Einstein. We also consider some open questions about his biography, and in particular his relations with other mathematicians and philosophers. The talk concludes with some considerations about Gödel’s health, particularly his psychiatric problems, which led to his ‘personality disturbances’ and ultimately to his death.
This talk is based to some extent on the recent book ‘Kurt Gödel – the Genius of Meta-mathematics’ (W.D. Brewer, Springer Scientific Biographies, 2022/23).

25.1. [GAUS-Kolloquium des CRC326]

(Teilnahme ggf. auch online möglich, Zugangsdaten über den Koll.beauftragten.)

Programm Sommersemester 2023

27.4. Prof. Dr. Hans Jockers (JGU Mainz)
The Quest of Hyperbolic 3-Manifolds in Mirror Symmetry

Abstract:
Mirror symmetry predicts the “classical“ algebraic and transcendental invariants of degenerate Calabi-Yau threefold to match with the symplectic “quantum” invariants of the mirror Calabi-Yau manifold. An instance of this correspondence arises from open-string mirror symmetry, in which algebraic cycles of the degenerate Calabi-Yau threefold correspond to Lagrangian submanifolds of the mirror manifold. I discuss this open-string mirror symmetry correspondence, and I illustrate how to calculate invariants in this context. These results propose a connection to hyperbolic 3-manifolds.

4.5. Prof. Dr. Felix Finster (Univ. Regensburg)
An introduction to causal fermion systems and the causal action principle

Abstract: The theory of causal fermion systems is an approach to describe fundamental physics. It gives quantum mechanics, general relativity and quantum field theory as limiting cases and is therefore a candidate for a unified physical theory. Moreover, causal fermion systems provide a general framework for modelling and analyzing non-smooth spacetime structures. The dynamics of a causal fermion system is described by a nonlinear variational principle, the causal action principle. In the talk I will give an introduction from the point of view of geometry and the calculus of variations.

11.5. Prof. Dr. Stefan Schröer (Univ. Düsseldorf)
Algebraic surfaces over the integers

Abstract: In this talk I give a gentle introduction to a general problem in arithmetic algebraic geometry:
What geometric objects can be defined by polynomials with integral coefficients such that no singularities arise over any prime field? After discussing the theorems of Minkowski, Tate, Ogg, Fontaine and Abrashkin I will explain some recent results on Enriques surfaces.

25.5. Prof. Alexander Kurganov (Southern University of Science and Technology, Shenzhen, China)
Low-Dissipation Central-Upwind Schemes

Abstract: The talk will be focused on central-upwind schemes, which are simple, efficient, highly accurate and robust Godunov-type finite-volume methods for hyperbolic systems of conservation and balance laws. I will first briefly go over the main three steps in the derivation of central-upwind schemes. First, we assume that the computed solution is realized in terms of its cell averages, which are used to construct a global in space piecewise polynomial interpolant. We then evolve the computed solution according to the integral form of the studied hyperbolic system. The evolution is performed using a nonsymmetric set of control volumes, whose size is proportional to the local speeds of propagation: this allow one to avoid solving any (generalized) Riemann problems. Once the solution is evolved, it must be projected back onto the original grid as otherwise the number of evolved cell averages would double every time step and the scheme would become impractical. The projection should be carried out in a very careful manner as the projection step may bring an excessive amount of numerical dissipation into the resulting scheme as was the case in previous versions of the central-upwind schemes.
In order to more accurately project the solution, we have recently introduced a new way of making the projection. A major novelty of the new approach is that we use a subcell resolution and reconstruct the solution at each cell interface using two linear pieces. This allows us to perform the projection in the way, which would be extremely accurate in the vicinities of linearly degenerate contact waves. This leads to the new second-order semi-discrete low-dissipation central-upwind schemes, which clearly outperform their existing counterparts as confirmed by a number of numerical experiments conducted for both the 1-D and 2-D Euler equations of gas dynamics in both single- and multifluid settings.
The accuracy of the low-dissipation central-upwind schemes can be further increased in two ways. First, we develop a scheme adaption strategy: we automatically detect „rough“ parts of the computed solution and apply an overcompessive slope limiter in these areas at the piecewise linear reconstruction step. The adaptive low-dissipation central-upwind schemes achieve a superb resolution in a variety of challenging numerical examples. Second, we utilize the new low-dissipation central-upwind numerical fluxes to construct new fifth-order finite-difference A-WENO schemes, which outperfom their existing A-WENO counterparts based on less accurate central-upwind numerical fluxes.

1.6. Prof. Dr. Thomas Schick (Göttingen):
Rigidity of scalar curvature

Abstract: The round metric on the n-dimensional sphere is very special.
By a celebrated theorem of Llarull, it has e.g. the property to be extremal
among metrics whose scalar curvature is nowhere smaller than the one of the sphere
(in the sense: one has to shrink the metric somewhere to increase the scalar curvature).
Indeed, this even holds if one allows to change the topology.
If n=2, this can be derived from the Gauss-Bonnet theorem, in higher dimensions one uses
the spectral theory of the Dirac operator.
We discuss these classical results and recent improvements (jointly obtained with Cecchini and Hanke)
which allow for metrics and comparison maps of low regularity.

15.6. Festkolloquium Manfred Lehn:

Coffee at 3pm in Hilbertraum (Details and program under this link)

Lectures by:
Prof. Dr. Dmitry Kaledin (HSE Univ. Moscow)
Geometry and topology of symplectic resolutions
Prof. Dr. Christoph Sorger (Nantes Univ.)
The topology of Hilbert schemes

22.6. Dr. Hans Fischer (Kath. Univ. Eichstätt)
Real Analysis 1830–1850: Propagation and Further Development of Cauchy’s Basic Concepts by Peter Gustav Lejeune Dirichlet

Abstract: Peter Gustav Lejeune Dirichlet (1801–859) is considered as one of the most significant promulgators of rigorous analytic standards in the pre-Weierstrass era. Through his studies in Paris (1822–1826) he became especially influenced by Cauchy’s „new“ analysis, and he adopted and modified its most important concepts, as one can see from some of his papers and in particular from lecture notes. In this talk I will explain in which way Dirichlet adapted or specified Cauchy’s notions of function, continuity including uniform continuity, and definite integrals in one and two dimensions. Finally, the question will be briefly discussed what influence Dirichlet actually had on the development of „epsilontic“ analysis.

Programm Wintersemester 2022/23

03.11. Prof. Dr. Wadim Zudilin (Radboud University Nijmegen)
Irrationality by experiment

Abstract: The majority of real numbers are irrational, however establishing this for very concrete numbers (like the values of Riemann’s zeta function and general L-functions at positive integers) remains a difficult task. In my talk I will (try to) give some insights into how Experimental Mathematics assists us in constructing good rational approximations to the quantities represented by period integrals.

10.11. Prof. Dr. Eduard Feireisl (Academy of Sciences, Prague)
The Euler system in fluid mechanics: Good and bad news

Abstract: We discuss some recent results concerning well/ill posedness of the Euler system describing the dynamics of a compressible viscous fluid. In particular, we address the following topics:
1. Density of the „wild“ data.
2. Euler system as an inviscid limit.
3. Measurable semigroup solution.

24.11. Dr. Emre Sertöz (Univ. Hannover)
Separating period integrals of quartic surfaces

Abstract: Periods form a natural number system that extends the algebraic numbers by adding values of integrals coming from geometry and physics. Because there are countably many periods, one would expect it to be possible to compute effectively in this number system. This would require an effective height function and the ability to separate periods of bounded height, neither of which are even remotely possible in general. I will, however, introduce a separation constant to numerically verify identities coming from integrals related to quartic surfaces in 3-space, i.e., related to K3 surfaces. This is joint work with Pierre Lairez.

1.12. Prof. Dr. Hartmut Monien (Univ. Bonn)
Dessins d’enfants and modular curves associated to the sporadic groups Co3 and Janko2 or how to solve a set of 276 polynomial equations of degree 276 in 276 variables explicitly

Abstract: Dessins d’enfants and their realization as Belyi maps of compact Riemann surfaces were originally discovered by Felix Klein. Their importance and relevance was finally understood by Alexander Grothendieck who rediscovered and named them in his „Esquisse d’un programme“ in 1984. The most important aspect of dessins is the operation of the absolute Galois group on them. Accordingly, dessins d’enfants provide fascinating insights and fundamental links between different fields of mathematics like inverse Galois theory, Teichmüller spaces, hypermaps, algebraic number theory and mathematical physics. The sporadic groups Janko 2 and Conway 3 are stabilizers of pair of lines in the 24-dimensional Leech lattice. In my talk I will show how to explicitly construct modular curves with automorphism groups J2 and Co3 using methods from applied mathematics.

08.12. Prof. Dr. Thomas Nikolaus (Univ. Münster)
Higher Algebra and algebraic K-theory

Abstract: This talk is about algebraic K-theory groups (defined by Quillen in the early 1970s). We will review the definition and motivation behind those groups and explain some applications.
Then we try to summarize what is known in terms of computations and explain some recent breakthroughs (based on so-called trace methods). One of the central tools used to achieve this progress is `higher categorical algebra‘ in the sense of Waldhausen, Lurie and others. As a sample application we cover the recent results on the K-theory of Z/p^n obtained in joint work with Antieau and Krause.

15.12. Brittany Shields, PhD (Univ. of Pennsylvania)
Scientific Diplomacy: Cold War Mathematicians and International Relations
Unfortunately, this talk had to be cancelled / der Vortrag musste leider abgesagt werden.

19.01. Dr. Hans Fischer (Kath. Univ. Eichstädt)
Real Analysis Around 1830/40: Propagation and Further Development of Cauchy’s Basic Concepts by Peter Gustav Lejeune Dirichlet
Unfortunately, this talk had to be postponed / wegen Erkrankung des Vortragenden muss der Vortrag auf einen späteren Termin verschoben werden.

26.01. Prof. Dr. Catharina Stroppel (Univ. Bonn)
From Platonic solids to Springer theory and beyond
Abstract: In this talk I want to give a small tour starting from Platonic solids and explain how one might naturally construct spaces/manifolds/varieties which arise in representation theory, more precisely Springer theory and sketch why representation theorists care. From that spaces we will construct a Fukaya type category. The talk is for a general audience.

02.02. Prof. Dr. Lutz Weis (Karlsruher Institut für Technologie)
Regularitätsabschätzungen für stochastische, parabolische Evolutionsgleichung

Abstract: Regularitätsabschätzungen sind wesentlich für den Halbgruppenzugang zu stochastischen, parabolischen Evolutionsgleichungen, die durch den Erzeuger einer analytischen Halbgruppe und einem Wiener Maß auf einem Banachraum mit der UMD Eigenschaft beschrieben werden, z.B. um geeignete Fixpunkträume für nichtlineare Gleichungen formulieren zu können.
Dabei wird eine neue stochastische Maximalfunktion eine wichtige Rolle spielen, um Ideen aus der harmonischen Analysis auf die stochastische Situation anpassen zu können.