Winter semester 2025/26:

27.11. Dr. Peter Gorzolla (Frankfurt)
Process support instead of plagiarism hunting. Dealing with AI in learning and teaching using the example of the AI strategy of the Frankfurt History Seminar

Abstract:

The ChatGPT shock at universities hit subjects in which academic writing plays a central role very early on. In the search for a pragmatic path between doomsday scenarios and sticking one’s head in the sand, which at the same time does not betray one’s own scientific principles, the History seminar was the first institute at Goethe University to adopt an AI strategy for learning and teaching in December 2024. This has since been disseminated to various other subjects at Goethe University as a basis for discussion and a concept template.

11.12. Professor 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-Theory

Abstract:

The study of continuous operations of groups such as GL(n;R) and GL(n;C) on Banach spaces leads to interesting algebraic questions. Great progress has been made in this area recently, and I will report on this.

15.1.: Festive colloquium on the occasion of the farewell of Dr. Cynthia Hog-Angeloni
Professor of 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 labeled oriented trees. Labelled oriented trees are algebraic generalizations 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 labeled 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. Professor of Rainer Kaenders (Bonn) unfortunately has to cancel due to illness of the lecturer!
The teacher education degree program in Bonn with a genetic introduction to infinitesimal calculus inspired by Otto Toeplitz

Abstract:
Since the winter semester 2017/18, we have established a one-year course “Fundamentals of Mathematics” for teaching degree students in the mathematics teacher training program at the University of Bonn, which consists of a lecture “Fundamentals of Mathematics I” (4 SWS) with practice classes (2 SWS) and an additional lecture course (2 SWS) “Calculation and Argumentation Techniques” and additional practice classes (2 SWS) in the winter semester (11 European Credit Transfer System). In the summer semester, the “Fundamentals of Mathematics II” (6 European Credit Transfer System credits) still consists of the lecture (2 SWS) with practice classes (2 SWS). In addition, the lecture “Linear Algebra” (4 SWS) with practice classes (2 SWS) is added with 9 European Credit Transfer System credits. This is followed in the second year by Analysis I, which is taken together with the first-year students of the Mathematics Bachelor’s program.
The lecture presents the Bonn mathematics teacher training program and deals with the content concept of the “Fundamentals of Mathematics”.

5.2. Prof. Dr. Alberto Cogliati (Padova Univ) unfortunately has to cancel due to illness of the lecturer!
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. Professor 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. Professor 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. Professor Dr. Amru Hussein (University of 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. Professor 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. Festive colloquium on the occasion of the 90th birthday of Prof. Dr. Albrecht Pfister
Spokesperson:
16:45h: Prof. Dr. Claus Scheiderer (University of Konstanz):
Hilbert’s 3-square theorem for ternary quartics: an elementary proof

Summary: In 1888 Hilbert published a fundamental work on sums of squares of real polynomials that would have a great influence on future developments. One of the main results states that any non-negative ternary form of degree four can be written as the sum of three squares of quadratic forms. Hilbert’s proof used subtle arguments from topology and algebraic geometry, some of which were far ahead of their time. In the early 2000s, Pfister became convinced that Hilbert’s theorem should also be provable using elementary Technics Departments. In joint work with the spokesperson, such a proof was found in the following years and was published in 2012. In my talk, I will outline this approach and will also explain to what extent further work by Pfister in recent years has led to an improvement.

17:45h: Professor Dr. Detlev Hoffmann (TU Dortmund):
The quadratic Zariski problem

Abstract: Pfister’s work on quadratic forms from the 1960s, in particular the so-called Cassels-Pfister partial form theorem, can be seen as the starting point of the theory of function bodies of quadrics, which was then systematically extended by Knebusch in the 1970s and underwent an enormous further development by new algebraic-geometric methods going back to Voevodsky and Rost in the 1990s. In this talk we will present a still unsolved problem from this field: the quadratic Zariski problem, in which the question is posed whether two stably birationally equivalent quadrics of the same dimension are already birationally equivalent
. We give a largely elementary introduction to the problem and present some recent results.

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. Professor of Christian Krattenthaler (Vienna):
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. at 3:30 p.m. “Departure to new fields of activity”
Farewell to Prof. Dr. Duco van Straten

19.04. (12 o’clock) 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 kernel.
This is joint work in progress with Ilia Gaiur.

2.5. inaugural lecture (16:00 h, Audimax)
Prof. Dr. Hendrik Ranocha (Mainz):
Numerical Mathematics

16.5. Professor Dr. Matthias Lesch (University of 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 been fully understood and it exhibits quite some interesting combinatorial features. I will report on a proof which was developed in a recent Master’s degree 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. Professor 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. Professor of Jochen Schütz (Hasselt University):
Aclass 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. Professor Dr. Peter Ullrich (University of Koblenz):
From Euler via Dirichlet to the Riemann zeta function

Abstract: The zeta series, which defines the zeta function named after Bernhard Riemann (1826-1866), was already investigated by Leonhard Euler (1707-1783): On the one hand, he determined their values for even natural arguments, and on the other, he gave the product representation named after him for them.
He also published both results in textbooks.
Gustav Lejeune Dirichlet (1805-1859) made explicit reference to the derivation of the product representation in the Introductio in analysin infinitorum in 1837 in his proof of the prime number theorem for arithmetic progressions. He also passed on his knowledge of Euler’s Mathematics writings to Riemann, who also referred to the product representation in his 1859 work “On the number of prime numbers under a given quantity”.
The lecture will analyze how the above results contributed to the emergence of analytic number theory.

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

Professor Dr. Peter Teichner (MPI Bonn)
A lecture à la Stephan Klaus

Abstract: We explain an elementary approach [Dold-Thom] to homology in terms of configuration spaces of charged particles. Many properties of homology, such as the Mayer-Vietoris principle, have very intuitive proofs, the cup product is quite simple.
paths in one of these configuration spaces are Feynman graphs and in fact there is a direct connection to the Mathematics theory of quantum observables in terms of factorization algebras [Costello-Gwilliam].
At the end of the lecture there is another connection, this time to generalized homology theories (configuration spaces provide usual homology with values in the abelian group of charges) and the Goodwillie calculus of analytic functors.

Prof. Dr. Wilderich Tuschmann (KIT):
Spaces and moduli spaces of Riemannian metrics

Abstract: Riemannian metrics exist on every differentiable manifold, but the existence or construction of metrics with certain given properties such as nonnegativity or negativity of sectional curvature, positivity of scalar or Ricci curvature, fulfillment of Einstein, Kähler or other special holonomy conditions, etc., on open or closed smooth manifolds have always been fundamental questions and problems in global differential geometry. Once these have been solved, they are directly followed by an equally important question in current research:
‘How many’ different metrics of such a type exist as a whole on the underlying manifold, and ‘how many’ different such geometries defined by it does it allow at all?
In my lecture, I will give an elementary introduction to this topic, on which Professor Klaus has also worked in particular, as well as a closer overview and insight into fundamental results and open questions in this field.

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 analyzing 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 analyzing 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. Professor 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. Inaugural Lectures (Helmholtz Institute conference room):
16:ooh:
Prof. Dr. Georg Tamme (Mainz)
Algebraic K-Theory
17:00h
Prof. Dr. Tom Bachmann (Mainz)
Motivic Topology

11.1. Professor Dr. Stephan Berendonk (Wuppertal):
From three learning environments to elementary geometry

Abstract: Congruence theorems, ray theorems, sum of angles in a triangle, Pythagoras and Thales. Even with this manageable wealth of school geometry experience, it is possible to be creative and exploratory in elementary geometry. The lecture will present three elementary geometry learning environments that can be used to experience different aspects of Mathematics. The first learning environment is about a competition of constructions, more precisely the classical constructions with compass and ruler. The second learning environment is about a kind of ‘imitation game’ in which we try to imitate classical proofs of the Pythagorean theorem as far as possible in the case of non-rectangular triangles, in the hope of obtaining proofs of the cosine theorem. In the third learning environment, the aim is to realize further geometric illustrations using suitable bar constructions based on the educational background of the pantograph, which embodies a centric extension. All three learning environments have a playful character and aim to create a corresponding image of Mathematics as an activity.

POSTPONEMENT to 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 Colloquium of CRC326.]

(Participation may also be possible online, access data via the coll. representative)

Program summer semester 2023

27.4. Professor 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. Professor Dr. Felix Finster (University of 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 modeling 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. Professor Dr. Stefan Schröer (University of 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 Enrique’s 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 outperform their existing A-WENO counterparts based on less accurate central-upwind numerical fluxes.

1.6. Professor 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. festive colloquium 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 (Catholic University of 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.

Program winter semester 2022/23

03.11. Professor 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. Professor of 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 (University of Hanover)
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. Professor Dr. Hartmut Monien (University of 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. Professor Dr. Thomas Nikolaus (University of 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 canceled.

19.01. Dr. Hans Fischer (Catholic University of 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 / due to illness of the speaker the talk has to be postponed to a later date.

26.01. Professor 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 those spaces we will construct a Fukaya type category. The talk is for a general audience.

02.02. Professor Dr. Lutz Weis (Karlsruhe Institute of Technology)
Regularity estimates for stochastic, parabolic evolution equation

Abstract: Regularity estimates are essential for the semigroup approach to stochastic parabolic evolution equations described by the generator of an analytic semigroup and a Wiener measure on a Banach space with the UMD property, e.g. to be able to formulate suitable fixed point spaces for nonlinear equations.
A new stochastic maximum function will play an important role in order to adapt ideas from harmonic analysis to the stochastic situation.