# Abstracts Minisymposia

## Clifford analysis and phase retrieval for image processing

###### Swanhild Bernstein, Freiberg, und Bettina Heise, Linz

In this minisymposiums, we will discuss recent results in Clifford analysis and its applications in image processing. Clifford analysis allows special constructions of function theory to be generalised to higher dimensions. In this way, one obtains new representations of multidimensional signals and a Fourier transformation adapted to the Clifford calculus. These theoretical results can be applied in particular to the essential problem of phase retrieval.

If conventionally one measures only the intensities of the EM wavefield or the magnitude of spatial power spectra, then phase retrieval is a classical tool to reconstruct the missed phase information. It is used in various application contexts, and the classical Gerchberg-Saxton method is one of the early famous implementations. It has since been developed into several versions of the iterative Fourier transform methods and further generalized by the iterative projection methods. Beyond current approaches in phase retrieval also Clifford analysis-based image processing can be used to extend these types of problems by (quaternion) phase retrieval and (quaternion) axis retrieval.

## Dynamics, stability and control in infinite dimensions

###### Jochen Glück and Andrii Mironchenko, Passau

The minisymposium aims at highlighting and discussing the interactions between three fields in mathematical analysis: operator semigroup theory, non-linear evolution equations and mathematical systems theory. We will discuss the recent developments on the long-term behaviour of operator semigroups, analysis of reaction-diffusion equations, and contemporary stability results from input/ouput-systems.

One overarching theme of the minisymposium will thus be the long-term behaviour of evolution equations, while a few talks on further related topics are included to provide a broader perspective.

## Fractional calculus in cancer modelling

###### Mabel Lizzy Rajendran and Christina Kuttler, München

The aim of the minisymposium is to provide motivation for considering fractional operators in cancer models and other cellular environments. Address the challenges these non local operators pose in terms of analysis and numerical simulation.

The tumour microenvironment has a strong influence on tumour cell proliferation and migration. For instant, the cell-cell adhesion induces subdiffusivity, hapotaxis and chemotaxis induces superdiffusivity, and the viscoelasticity of the extracellular matrix substantially affect the spreading, growth, proliferation, migration of the cancer cells.

Fractional operators have undoubtedly exercised their efficiency in modelling complex and intermediate processes like anomalous diffusion (sub and super diffusion) and viscoelasticity. At the same time, the very nature of non-locality of the fractional operators introduces computational complexities and challenges in obtaining existence results. This calls for the analysis of these equations and efficient memory management algorithms for simulation. This minisymposium, therefore, paves way to bring together the two communities of researchers, who are working in cancer modelling and who have knowledge on fractional operators, to share knowledge, create synergies to explore these directions of research.

## Functional analytical approaches to dynamical systems

###### Christian Pötzsche, Klagenfurt, und Nils Waterstraat, Halle

The aim of this minisymposium is to bring together researchers working in Functional Analysis and Dynamical Systems. The talks cover a variety of topics including spectral theory, bifurcation theory for discrete and continuous dynamical systems, Hamiltonian systems as well as ramifications to Floer homology.

## Large cardinals

###### Philipp Lücke, Barcelona, und Sandra Müller, Wien

This minisymposium will be devoted to recent developments in the theory of large cardinals, a central concept of contemporary set theory that allows the measurement of the consistency strength of mathematical theories and the ordering of these theories into a canonical hierarchy. Seminal results show that large cardinal assumptions themselves answer many important questions left open by the standard axiomatization of set theory and this leads many set theorists to think that these axioms should be included in the correct axiomatization of mathematics. In the last fifty years, set theorists have developed a deep and canonical theory of large cardinals and, in recent years, breakthrough results in vastly different regions of the large cardinal hierarchy were obtained.

The talks in our symposium will cover this wide spectrum of research, from virtual large cardinal axioms in the lower reaches of this hierarchy all the way up to axioms of infinity that contradict the Axiom of Choice.

## Loop spaces in geometry and topology

###### Sebastian Boldt, Leipzig, and Batu Güneysu, Potsdam

The aim of this minisymposium is to present recent results on the loop space of a closed (Riemannian) base manifold that highlight the intimate connection between the topology / geometry of the loop space with the topology / geometry of its base manifold.

Firstly, we would like present recent results obtained by Sergio Cacciatori, Batu Güneysu and Matthias Ludewig, who have constructed a theory of integration of differential forms on the loop space of a closed even-dimensional Riemannian spin manifold. This construction relies on new methods from noncommutative geometry and Chen integrals and it admits a Duistermaat-Heckman localization formula, which allows an entirely geometric proof of the Atiyah-Singer index theorem, confirming conjectures by Atiyah and Witten.

Secondly, we would like to present a recent result by Philippe Kupper, who has constructed a transfer product on the homology of the quotient of the loop space over a sphere by a finite subgroup of O(2), which might provide a first step towards the existence of infinitely many closed geodesics for any reversible Finsler metric on a sphere.

## Massively parallel methods in geometry and applications

###### Janko Böhm, Kaiserslautern and Anne Frühbis-Krüger, Oldenburg

High performance computing is an essential tool for numerous current scientific research problems. In this minisymposium, we discuss efforts to bring this technique to new application areas, in particular elaborate algorithms from geometry and algebra. Recent developments like the combination of the workflow management system GPI-Space with computer algebra software into a framework for massively parallel computation have made such approaches accessible to the mathematician, eliminating the need to deal with intricate technical details. The minisymposium has the goal to bring together researchers pioneering this approach in different areas, discussing the current state of the art and possible future developments. We plan to address applications in classical algebraic geometry, singularity theory, combinatorics, and high energy and solid state physics.

## Mathematik für die Bildverarbeitung

###### Jürgen Frikel, Regensburg, Martin Storath, Schweinfurt and Brigitte Forster, Passau

Zahlreiche Bildgebende Verfahren und Methoden der Bildverarbeitung wären ohne Mathematik nicht möglich. So bildet beispielsweise die Fouriertransformation die mathematische Grundlage für die Magnetresonanztomographie und die Radon-Transformation dient als Modell für die Computertomographie. Daneben basieren viele effiziente Algorithmen auf Ergebnissen und Fortschritten in der Optimierung.

In diesem Minisymposium wollen wir die neuesten mathematischen Entwicklungen in der Bildverarbeitung und inversen Problemen der Bildgebung zusammentragen. Unter anderem möchten wir den Austausch über neue Ansätze zur Transformationsentwicklung, variationelle Methoden sowie mathematische Analyse von Learning-Verfahren in der Bildverarbeitung fördern.

## Mathematische Analyse komplexer Quantensysteme

###### Heinz Siedentop, München, und Volker Bach, Braunschweig

Dieses Minisymposium wird sich vor allem auf analytische und stochastische Methoden beziehen, die für große wechselwirkende Quantensysteme – insbesondere solche mit realistischer Wechselwirkung wie Coulombpotentiale – relevant sind. Die Motivation geht dabei von der Quantenfeldtheorie, der Theorie der kondensierten Materie sowie der Atom- und Molekülphysik aus. Es handelt sich sowohl im statische Probleme, die mit spektraltheoretischen und stochastischen Methoden behandelt werden als auch um dynamische Probleme wie der Herleitung effektiver Einteilchengleichungen. Typischer Weise handelt es sich um die kontrollierte Approximation eines hoch – oder sogar unendlich – dimensionalen Problems durch eine – wenn auch nichtlineare – Gleichung in fixer, typischer Weise drei, zwei oder einer Dimension. Einfache Beispiele solcher Gleichungen sind die Thomas-Fermi-Gleichung im statischen Fall sowie die Wlassow-Gleichung. Neben der Herleitung wird es auch um die Lösungstheorie solcher effektiven Gleichungen gehen.

Ein weiteres Feld ist die Quanteninformationstheorie.

## Meta-learning for randomized optimization heuristics

###### Carola Doerr, Martin Krejca, Paris, and Maximilan Moll, München

Randomized optimization heuristics, such as Simulated Annealing or evolutionary algorithms, are applied very successfully to a wide range of complex optimization problems. Key to the success of each heuristic is its distribution from which it draws new candidate solutions. Modern heuristics use feedback from prior solutions to dynamically adjust their distribution during the optimization process. Such update strategies range from rather simple success-based rules to complex strategies combining static as well as dynamic information. Similar approaches can be found in Reinforcement Learning, however applied to dynamic optimal control problems. While several types of evolutionary algorithms can be used for their solution, the field generated its own approaches to learning optimal behaviour as well.

The goal of this minisymposium is to bring together researchers interested in the theoretical performance analysis of randomized optimization heuristics with researchers interested in learning. No prior knowledge about heuristic search is assumed, and the speakers provide enough background to enable participants to grasp the main ideas.

We leave ample time for discussions, as we hope to kick-start further discussions on learning-based approaches for the dynamic parameter adjustment of optimization heuristics.

## Model order reduction and approximation of coupled systems

###### Björn Liljegren-Sailer, Trier, and Benjamin Unger, Stuttgart

The simulation and control of coupled systems are relevant in various applications, such as, e.g., the modeling of gas transport networks, electromagnetics, or mechanical systems. This minisymposium focuses on the efficient approximation of such systems by model order reduction and data assimilation techniques. The focus lies on the treatment of network aspects and the interpretability of the resulting approximations.

## New trends in algorithmic randomness and computable analysis

###### Rupert Hölzl, München, und Christopher Porter, De Moines, USA

The aim of our panel is to highlight a range of new developments in algorithmic randomness and computable analysis, two sub-branches of computability theory. In the theory of algorithmic randomness, one studies definitions of random objects (typically finite and infinite sequences), with the key feature of these definitions being that they are given in terms of effectively computable procedures. On this approach, for instance, one can define a sequence to be random if it passes all effectively presented statistical tests, if it cannot be compressed by any effective procedure, or if it cannot be predicted by any computable method of prediction. Computable analysis, a closed related area, applies the machinery of computability to study the effective content of results from classical analysis.

Talks featured in our minisymposium will cover a range of topics in these two fields, including effective Hausdorff dimension, the study of normal numbers, random trees, and notions of computational depth.

## Nonlocal conservation laws

###### Simone Göttlich und Jan Friedrich, Mannheim

In recent years, conservation laws with nonlocal flux have gained a lot of interest in research. They are suitable to describe several complex dynamics, such as vehicular traffic, material flow, crowd motion, supply chains or sedimentation. Since standard theory often fails in this setting, there is a strong need to develop new mathematical tools and methods for investigating the nonlocal behaviour. Current research focuses on studying existence and uniqueness of solutions, convergence of numerical schemes and the connection to the class of well-established local conservation laws.

With this minisymposium we aim to provide a platform for researchers working with nonlocal conservation laws to present their current research results. Moreover, we hope to stimulate discussions leading to new research directions and hopefully foster new collaborations among junior and senior scientists.

## Optimal transport revisited

###### Jonas Hirsch und Tobias Ried, Leipzig

The aim of this minisymposium is to present recent results in optimal transportation, exploring regularity theory and applications. We want to give room for diverse approaches, for instance contrasting PDE and recent variational techniques. We plan to visit its applications in branched transport, martingale problems and density functional theory.

We want to bring together scientists with various views on optimal transport to foster scientific exchange and explore new developments in the field.

## PDE models describing interfaces and complex structures

###### Patrik Knopf, Regensburg, und Stefan Metzger, Erlangen

Complex structures and interfaces separating different materials or physical states play an important role in many technological applications like lab-on-a-chip devices or liquid-crystal displays. Further well-known applications are models describing tumor growth, biological membranes, two-phase flows, fluid-structure interactions, and fluid flow in porous media. In this minisymposium, we want to highlight recent advances in modeling as well as in the analytical and numerical investigation of PDEs describing interfaces and complex structures.

## Recent developments in mathematical fluid dynamics

###### Christian Zillinger und Xian Liao, Karlsruhe

Fluid dynamics are a rich mathematical topic in partial differential equations bringing together numerous different perspectives, modelling and intricate analysis.

It is the aim of this minisymposium to discuss recent results in the field both by junior and senior researchers, to highlight different perspectives and to build new connections.

## Signal processing and feature extraction

###### Thomas Fink und Florian Heinrich, Passau

Signal processing is a field with a variety of facets, many of which recently became increasingly important in order to create the mathematical and algorithmic background for a plethora of current technological advances e. g. in biomedical imaging, AI, audio and video processing. The aim of this minisymposium is to bring together young researchers and established experts in the field of signal processing both from Austria and from Germany for fruitful discussions and a vivid exchange of ideas. The joint meeting of ÖMG and DMV offers a wonderful opportunity for us to implement this transgenerational idea in the form of the planned minisymposium.

## Structure-preserving computational methods

###### Ashish Bhatt, Dhanbad, Indien

The exact meaning of the word “structure” is usually discipline-dependent, but it is often associated with the qualitative properties of a physical system and its mathematical formulation. This theme of structure preservation is prevalent in computational methods and scientific computing and cuts across vast swathes of embedded disciplines. Structure-preserving computational methods focus more on imitating the underlying qualitative properties of a system rather than improving the quantitative accuracy of a method for the system. Their advent can be traced back to devising structure-preserving numerical methods for differential equations. Such methods have also been devised to preserve the qualitative behavior through model order reduction. Lately, there has been a significant interest in structure-preserving neural networks mimicking various complex physical systems. Structure-preserving methods are also utilized, e.g., in numerical linear algebra in matrix decompositions. This minisymposium aims to further the discourse on this topic by inviting discussions on the latest developments in this field.

## AIMS-Germany minisymposium on applied mathematics

###### Vladimir Shikhman and Alois Pichler, Chemnitz; Mouhamed Moustapha Fall and Franck Kalala Mutombo, M'Bour, Sénégal

The AIMS-Germany Minisymposium is devoted to the current research in the area of Applied Mathematics conducted by researchers from the African Institute for Mathematical Sciences (AIMS) network and their partners in Germany (https://nexteinstein.org).

The participants, mainly Phds and Post-Docs, will have an opportunity for international networking and visibility while presenting their research results. Due to Corona virus, the Minisymposium will be held online as part of 2021 Annual Meeting of German Mathematical Society in Passau. It is planned to award three DAAD prizes of 500 Euros each for the best presentations.

## Connecting young researchers by networks

###### Mechthild Thalhammer, Innsbruck, and Veronika Pillwein, Linz

This mini-symposium is organised by Veronika Pillwein and Mechthild Thalhammer as representatives of the network A^2WiM (Austrian Association of Women in Mathematics), which has been created in 2020 to bring together female mathematicians in Austria and foster interdisciplinary collaborations as well as mutual support such as career advice and mentoring.

The intention of the mini-symposium is to initiate in particular the scientific exchange between young mathematicians of all genders from Austrian and German institutions and to promote new perspectives. The connecting element is a common research interest in graph and network theory.

This theme is of high relevance in different areas of application ranging from computer science over natural sciences to social science. Various mathematical subdisciplines such as discrete mathematics, ergodic theory, and stochastics provide diversified approaches for the study of open questions. Survey talks will be given by advanced researchers.

## Examining mathematics with electronic systems (E-Assessment)

###### Helena Barbas and Julian Großmann, Hamburg

This minisymposium is about e-assessment in mathematics. Over the last years, many different possibilities for electronic tests and exams have arisen. Especially for mathematical topics, it is quite interesting how electronic equipment can be used to check for understanding. With randomization, it is possible to offer infinitely many training exercises and also equivalent exam questions without changing the core of a question. There are also different approaches to design questions that check mathematical proofs and adaptive questions where intermediate results are marked. We present different mathematical tools, software and approaches of e-assessment for teaching courses in mathematics, like Numbas, STACK, WeBWorK, Möbius, Mumie, Onyx, ILIAS, and others, as well as examples how classical assessment in mathematics can be mapped to electronic assessment.

## Get-together and career advice for young mathematicians

###### Hana Dal Poz Kouřimská, Wien, and Teresa Heiss, Wien

In the times of the COVID pandemic networking is especially challenging for young scientists. We would like to give young scientists the opportunity to get to know each other. To this end, we – the Austrian Association of Women in Mathematics (A²WiM) – offer to organize a virtual Young Scientists' Meeting at this year’s DMV ÖMG Annual Conference, open to people of all genders.

The focus of the meeting is on networking and career opportunities. The program consists of: Discussion of career opportunities in and out of academia, Networking within specific fields of mathematics, An evening get-together.

## Historische Aspekte numerischer Methoden in Theorie und Praxis

###### Hans Fischer, Eichstätt, and Ysette Weiss, Mainz

Die Entwicklung numerischer Methoden ist durch die Notwendigkeit einer ökonomischen Rechenpraxis, aber auch in vielen Fällen bereits durch die Unmöglichkeit motiviert, überhaupt exakte mathematische Ergebnisse erzielen zu können. In dem Symposium soll ein Einblick in verschiedene Aspekte der numerischen Mathematik aus historischer Sicht gegeben werden: Die Notwendigkeit approximativer Bestimmung, numerisches Rechnen in der Astronomie (wir feiern Keplers 450. Geburtstag am 27. Dezember), spezielle Reihenentwicklungen, Rechenmaschinen, institutionelle Verankerung bis hin zur Disziplinbildung der „Angewandten Mathematik“.

## Mathematical proof in an exam

###### Thomas Skill, Bochum, and Walther Paravicini, Tübingen

Proving a mathematical statement is a central capability in a mathematical course. This is why the importance of exercises and exams seem to be obvious.

But why do we test that in exams? Mathematicians do not prove a theorem in a limited time. So there might be other motivations for testing such abilities (to solve a problem in a limited time). If we are aware of these, we will be able to form our teaching and the demands of complexity in an appropriate way.

An answer to this questions should inform our teaching and help us to determine the right complexity of the requested proof.

The first talk gives an overview of the different aspects of the topic. Then we take this as objective of our teaching and analyze it in the model of constructive allignment.

In the third talk we present best practise examples and invite the audience to contribute their experiences. The last speaker shows us how we can construct electronic tasks to assess argumentation skills.

## Mathematics and arts

###### Milena Damrau, Bielefeld, and Martin Skrodzki, Delft

This minisymposium aims to bring together researchers interested in the connection of mathematics and arts. The talks present artistic objects that include mathematical components and put a focus on the imparting of this underlying mathematics. Furthermore, they explore mathematical themes that invite discussions of their illustrations and the embodied artistic value. A variety of topics centred around the inclusion of mathematics in different art forms like painting, sculpture, architecture, textiles, and music are covered. Moreover, we discuss uses of these combinations for example in high school and university teaching or in outreach projects directed at the general public.

## Mathematik in der Informatik

###### Veronika Böhm, Marion Christl and Bejamin Huber, Passau

Die IEEE Student Branch Passau präsentiert verschiedenste Vorträge aus der Informatik mit Bezug zur Mathematik – u. a. ‘Style Transfer AI - Wie neuronale Netze Kunst erzeugen‘ sowie einen Vortrag zum Hochleistungsrechner ‘SuperMUC‘ etc. Kooperationen mit regionalen Firmen und Forschungsinstituten ermöglichen dabei einen besonderen Fokus auf anwendungsnahe Forschungsthemen - auch aus der Wirtschaft. Mit einem breit gefächerten Themengebiet sollen (eventuell auch als Ergänzung zur Studierendenkonferenz) besonders Studierende und Doktorand:innen, aber auch alle an der Mathematik, Informatik oder Elektrotechnik Interessierte angesprochen werden.

## Ready for MaRDI, am I a digital mathematician?

###### Karsten Tabelow und Thomas Koprucki, Berlin, sowie Moritz Schubotz und Olaf Teschke, Karlsruhe

Have you seen yourself typing $$ in an Email or did you miss the possibility to search for a mathematical formula in Google? If yes, you are already on your way to become a digital mathematician. The good news is, you are not alone and many mathematicians also use computers to obtain mathematical results.

The mathematical research data initiative (MaRDI) in Germany aims to connect those people and facilitates the sharing and finding of mathematical research data and mathematical knowledge. MaRDI aims to establish best practices and low-barrier infrastructures for mathematicians to better organize and access large amounts of data and knowledge. MaRDI aims to integrate individual results, e.g., as contained in a paper, into a common knowledge base like Wikipedia. In this minisymposium, we present the state-of-the-art and lessons learned from practical experience in handling mathematical research data and information. We invite mathematicians to share and discuss their experiences, needs, concerns and perspectives on the digital transformation and the innovations necessary to drive it across all levels of the mathematical ecosystem covering students, researchers, reviewers and funding bodies.

## Thinking about proofs

###### Deniz Sarikaya, Hamburg

Thinking about proofs: formal, philosophical, linguistical and educational perspectives

It is often said that all of mathematics can be reduced to first-order logic and set theory. The derivation indicator view says that all proofs stand in some relation to a derivation, i.e., a mechanically checkable syntactical objects following fixed rules, that would not have any gaps. For a long time this was a mere hope. There may have been proofs of concepts from early logicists but derivation never played a big role in mathematical practice. The modern computer might change this. Interactive and automated theorem provers promise to make the construction of a justification without any gaps feasible for complex mathematics.

This minisymposium brings together philosophers, educators and linguists to study both proofs as they can be found in real textbooks as well as in the logical sense, i.e., derivations.

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