# Seminars and workshops

## Dates for seminars in the winter semester 2020/21

Registration for seminars for the winter semester 2020/21 will take place via a new matching system. Therefore, there will be only one round instead of the usual two rounds.

3 July 2020: Program announced for winter semester 2020/21

13 July (12:00 pm) - 19 July 2020: Students register using the matching system

21 July - 26 July 2020: Lecturer's selection round

29 July: results are available in the matching system

from 3 August: Allocation of remaining places

## How are seminar places allocated?

The allocation of places in the workshops and seminars takes place in two stages:

You register using the matching system during the current semester for one of the seminars or one of the workshops offered in the following semester. The supervising tutors make a selection from the list of applicants. In the matching system you can see in which seminar you have been allocated a place.

If you were not allocated a place in the matching or if you would like to take part in a second seminar, please submit an informal application after the matching indicating your preferences from the remaining seminar places to:

- bachelor (at) ma.tum.de - for workshops and Bachelor’s advanced seminars

- master (at) ma.tum.de - for Master's advanced seminars

## Seminars for Bachelor's students

For each seminar offered to Bachelor's and Master’s students, there is a separate registration process in the matching system. Please only register for seminars labeled "Bachelor". Places in the seminars labeled "Master" are reserved for Master’s students who are already enrolled in these degree programs.

After the selection round, you can register for available places in the Master’s advanced seminars. In order to do so, please submit an informal application to master (at) ma.tum.de.

## Bachelor's seminars offered in the winter semester 2020/21

#### Language

#### Number of places

#### Content

Spin glass models are archetypes for complex cost landscapes. They are discussed in a variety of applications from physics, neural networks to computer science. In this seminar you will be introduced to mean-field spin glasses as the random energy model, the Sherrington- Kirkpatrick glass and the Hopffield model for neural networks. Discussing properties of these models you will be introduced to a broad set of mathematical techniques such as concentration of measure estimates, variational methods or elements of the theory of point processes.

#### Requirements

Introduction to Probability Theory [MA1401] Probability theory [MA2409]

#### Literature

We will mostly follow Part III in: A. Bovier, Statistical mechanics of disordered systems: a mathematical perspective, Cambridge UP 2012.

#### Informations

#### Language

#### Number of places

#### Content

In this seminar, we will discover efficient and elegant algorithms for discrete optimization problems that go beyond what is taught in introductory courses. We will cover topics such as matchings in non-bipartite graphs, matroid intersection, submodular function minimization, as well as approximation algorithms for knapsack, facility location, or sparsest cut.

#### Requirements

"Algorithmische Diskrete Mathematik" or some equivalent introduction to basic algorithms

#### Literature

Korte, Vygen - Combinatorial Optimization

#### Informations

#### Language

#### Number of places

#### Content

Algebraic Geometry is an intriguing and modern subject with relations to many areas of pure mathematics such as topology, number theory, representation theory, complex geometry, but also to theoretical physics. Classically, algebraic geometry was the study of the geometry of the sets of zeroes of systems of polynomial equations. The field dramatically changed in the 60s and 70s when Grothendieck replaced the previously studied notion of algebraic varieties by his much more general notion of schemes. This new language at first seems to be more technical, and is more abstract. However, it turns out that this approach is in fact more elegant, and at the same time offers much more powerful methods. In the sequel it rapidly became the generally accepted language for this subject, and a rich theory has been developed. This course is an introduction to Algebraic Geometry. In the seminar we will review of some basic theory of algebraic varieties, introduce the spectrum of a ring, study sheaves and locally ringed spaces, and introduce schemes and some of their basic properties. We will see examples such as curves and affine and projective spaces.

#### Requirements

Algebra, Commutative Algebra

#### Literature

There are many books on the subject, for example: D. Eisenbud, J. Harris: The Geometry of Schemes U. Görtz, T. Wedhorn: Algebraic Geometry I R. Hartshorne: Algebraic Geometry D. Mumford: The red book of varieties and schemes

#### Informations

This seminar (2SWS, Bachelor and Master) is taking place twice a week in the first half of the semester. In the second half of the semester there will be a lecture (2SWS) taking place twice per week, at the same time and place as the seminar, and continuing with the subject. Exercise sessions for the lecture (2SWS) will be taking place once per week for the whole semester. In the first half we review the necessary background for the lecture (i.e. do exercises on the material of the seminar), in the second half these are "usual" exercise sessions. You can participate in the seminar, or in the lecture (including the exercise sessions), or in both, they are formally independent courses. If you want to have credit for the seminar you need to register and give a talk, if you just want the material as preparation for the lecture you can attend without registration.

#### Language

#### Number of places

#### Content

Das Seminar ist ein gemeinsamer Lektüre- und Diskussion-Kurs des Buches "Algorithms from the Book" von Kenneth Lange (SIAM, 2020). Es beschäftigt sich mit berühmten und erfolgreichen Algorithmen und ihren mathematischen Grundlagen.

#### Requirements

Solide Kenntnisse in Analysis und linearer Algebra, Grundkenntnisse in Numerik

#### Literature

Kenneth Lange, Algorithms from the Book, SIAM, 2020 (Über die Bibliothek können Sie auf eine digitale Version des Buchs im Volltext zugreifen.)

#### Informations

Weitere Informationen finden Sie unter https://www-m8.ma.tum.de/foswiki/pub/M8/Allgemeines/CarolineLasserTeach/Seminar_OscQuad_SS20.pdf?=t=12

#### Language

#### Number of places

#### Content

Verallgemeinerte Lineare Modelle, Verallgemeinerte Additive Modelle, Kredibilitätstheorie, Neuronale Netzwerke, Klassifikationsbäume, Ensemble-Learning Methoden, Stützvektormethoden

#### Requirements

MA2402

#### Literature

Wüthrich, M. V. and Buser, C. (2018): Data Analytics for Non-Life Insurance Pricing. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2870308

#### Informations

Online Seminarvorbesprechung am 17.07.2020 um 16:00. Mehr Informationen sind unter https://www.groups.ma.tum.de/mathfinance/lehre/wintersemester-202021/

#### Language

#### Number of places

#### Content

The Expectation-Maximization (EM) algorithm is a popular optimization algorithm for computation of maximum likelihood estimates in statistical models for incomplete data. Examples of applications include mixture models, hidden Markov models, factor analysis and other latent variable models. The seminar participants will present classic papers introducing the EM framework and its applications, as well as recent work that gives statistical guarantees for estimates computed using EM.

#### Requirements

Probability Theory, Basic Statistics. For Master students: Computational Statistics.

#### Literature

Papers including A.P. Dempster, N.M. Laird, D.B. Rubin (1997). Maximum likelihood from incomplete data via the EM algorithm. With discussion. J. Roy. Statist. Soc. Ser. B 39(1):1-38. C. Jin, S. Balakrishnan, M.J. Wainwright, and M.I. Jordan (2016). Local maxima in the likelihood of Gaussian mixture models: Structural results and algorithmic consequences. In NIPS Conference. S. Balakrishnan, M.J. Wainwright. B. Yu (2017). Statistical guarantees for the EM algorithm: from population to sample-based analysis. Ann. Statist. 45(1): 77-120.

#### Informations

Preliminary meeting intended for early August 2020.

#### Language

#### Number of places

#### Content

Functional inequalities compare integral expressions. An elementary example is Hölder's inequality that estimates the integral of a product of two functions by a product of the integrals of appropriate powers of the individual functions. In the seminar, we prove a variety of far more sophisticated functional inequalities, for instance those that go by the names of Young, Hardy-Littlewood-Sobolev, or logarithmic Sobolev. The proofs are partially ingenious, using deep geometric constructions, hidden symmetries and non-obvious dualities. We shall also discuss applications of these inequalities in differential geometry (e.g. curvature bounds) and physics (rate of equilibration in particle systems).

#### Requirements

Participants should have completed the introductory lectures Analysis 1+2 as well as the one on measure and integration. Knowledge from the courses on functional analysis and/or PDEs are occasionally helpful, but are not needed.

#### Literature

We shall use the book E.Lieb und M.Loss: "Analysis" (GSM 14, AMS) as our main source. For more advanced talks, I can provide a plentitude of current research articles.

#### Informations

#### Language

#### Number of places

#### Content

Massive testing is an important ingredient to control infectious diseases such as the current COVID-19 pandemic. Group testing methodologies, where multiple different specimens are tested as a pool using a single test, can help increase the efficiency by reducing the number of required tests. In this seminar, we will study the extensive mathematical literature regarding the problem of determining appropriate designs of the group testing protocol. In particular, we aim to cover under which assumptions group testing makes sense at all, and if yes, which group size is optimal.

#### Requirements

MA5441 Fundamentals of Statistics

#### Literature

Ding-Zhu Du, Frank Kwang Hwang. Combinatorial Group Testing and Its Applications, World Scientific, 1993 Ding-Zhu Du, Frank Kwang Hwang. Pooling Designs And Nonadaptive Group Testing: Important Tools For Dna Sequencing, World Scientific, 2006 Matthew Aldridge, Oliver Johnson, Jonathan Scarlett. Group testing: an information theory perspective Now Publishers, 2019 Further literature for each seminar topic will be provided to the participants in the form of research articles.

#### Informations

The seminar will take place in blocks on 3-5 afternoons throughout the semester.

#### Language

#### Number of places

#### Content

This seminar will provide an introduction to the theory of quantum computing, focusing on algorithms. We will cover the fundamentals of quantum mechanics and discuss known quantum algorithms and their properties. This includes Shor's algorithm, algorithms for the hidden subgroup problem, Grover's search algorithm and various related oracle-based quantum speedups.

#### Requirements

Analysis 1&2, Lineare Algebra 1&2, Einführung in die diskrete Mathematik.

#### Literature

Literature: Primarily Ronald de Wolf, Quantum Computing: Lecture Notes, arXiv:1907.09415. Additional literature TBD.

#### Informations

This seminar will be held as a block-seminar at the beginning of term. See https://www-m5.ma.tum.de/Allgemeines/Lehrveranstaltungen for additional information.

#### Language

#### Number of places

#### Content

In recent years, there has been an increasing interest in topics at the intersection of economics and computer science, as witnessed by the continued rapid rise of research areas such as algorithmic game theory and computational social choice. This development is due to the emergence of computational networks such as the Internet as well as the need to get a grip on algorithmic questions in economics. In this seminar, we will deal with both the theoretical foundations as well as their computational properties and possible applications.

#### Requirements

It is expected that participants are experienced in formally proving mathematical statements and are familiar with standard proof techniques. Additionally, basic knowledge of complexity theory is useful (e.g., module IN0011).

#### Literature

The seminar will mostly be based on the books Economics and Computation by David C. Parkes and Sven Seuken and the Handbook of Computational Social Choice. Both books will be available for free download for participants of the seminar in our Moodle course http://go.tum.de/612829 via the guest key provided during the seminar overview meeting.

#### Informations

There will be a seminar overview (Vorbesprechung) online meeting on Friday, July 10, 2020. All students have to apply for the seminar. Further information (including the application procedure) can be found in the course homepage: go.tum.de/291400

#### Language

#### Number of places

#### Content

The seminar will provide a mathematical introduction to the following topics: - Foundations of supervised learning - Representation and approximation capabilities of neural networks - Training of neural networks - The unreasonable effectiveness of neural networks

#### Requirements

Analysis 1&2, LADS 1&2, Grundlagen in Statistik und/oder Wahrscheinlichkeitstheorie

#### Literature

Literatur wird individuell bekannt gegeben.

#### Informations

Das Seminar findet geblockt an vier Terminen (vorauss. November 2020) statt.

#### Language

#### Number of places

#### Content

Not only in times of COVID-19, communicable diseases were big threats to populations. A better, quantitative understanding of these processes help also to develop defense strategies or how to optimise treatments. Different mathematical tools may be appropriate as modelling approaches. In the seminar, we will mainly focus on Ordinary differential equations and Partial differential equations Often, the dynamic behaviour for whole populations is described by differential equation models. PDEs allow e.g. for considering spatial models. For small populations, stochastic models may be more appropriate. We will discuss typical modelling approaches including their analysis as well as concrete examples for diseases (like Influenza, HIV, and Tuberculosis). This seminar will be based on parts of the book “Mathematical Models for Communicable Diseases” by Fred Brauer and Carlos Castillo-Chavez and further original papers in this context dependent on the interests and previous knowledge of the participants.

#### Requirements

Mathematical models in Biology, Knowledge in Ordinary differential equations

#### Literature

Fred Brauer, Carlos Castillo-Chavez: Mathematical Models for Communicable Diseases, SIAM 2013 and other publications in this context

#### Informations

Further organisation, e.g. choice of preferred topic for the talk etc. will be done after the group of participants is fixed. Questions are always welcome!

#### Language

#### Number of places

#### Content

Die Studierende bereiten die mathematischen Grundlagen der in der Chemometrie angewendeten Verfahren auf und wenden sie auf ein Anwendungsbeispiel an. Insbesondere das Aufzeigen der Grenzen der Verfahren steht im Vordergrund. Eine praktische Programmieraufgabe in MATLAB oder R ist Teil der Ausarbeitung.

#### Requirements

Bereitschaft, sich in ein Thema einzuarbeiten.

#### Literature

Wird bei der Vorbesprechung (Videokonferenz in der letzten Semesterwoche) bekannt gegeben.

#### Informations

Das Seminar wird als Webinar abgehalten. Der Seminarvortrag ist als Video, das man als Tutorial für die besprochene Methode verwenden kann, vorzubereiten.

#### Language

#### Number of places

#### Content

In diesem Seminar werden wir uns mit dem Abzählen, der Existenz und der Konstruktion verschiedener diskreter Konfigurationen beschäftigen. Typische Vertreter davon sind etwa Partitionen, Halbordnungen, Permutationen und Graphen. So eingängig kombinatorische Problemstellungen sind, so knifflig aber auch elegant erweisen sich oft ihre Lösungen. Basierend auf ausgewählten Themen wollen wir grundliegenden intuitiven sowie methodischen Zugang zur Kombinatorik erlagen.

#### Requirements

Analysis 1/2, Lineare Algebra (und Diskrete Strukturen) 1/2

#### Literature

Jacobus van Lint, Richard M. Wilson: A Course in Combinatorics. Cambridge University Press, 2001. Konrad Jacobs, Dieter Jungnickel: Einführung in die Kombinatorik. de Gruyter, 2004. Peter Tittmann: Einführung in die Kombinatorik. Springer Spektrum, 2014.

#### Informations

Weitere Details werden hier bekannt gegeben: https://www.or.tum.de/en/teaching/winter2020/kombinatorik/

#### Language

#### Number of places

#### Content

Dieses Seminar widmet sich aktuelle Entwicklungen der nichtlinearen Optimierung und bereitet zudem auf eine Bachelor- oder Masterarbeit in diesem Gebiet vor. In den Vorträgen werden insbesondere aktuelle Themen aus folgenden Bereichen der nichtlinearen Optimierung behandelt: Neue Entwicklungen in Theorie und Methoden der Optimierung, speziell auch in den Bereichen Data Science und Machine Learning; innovative Anwendungen in Technik, Natur- und Wirtschaftswissenschaften, KI, etc. English version: This seminar addresses recent advances in nonlinear optimization and also serves as a preparation for a Bachelor's or Master's thesis in this field. The seminar covers the following topics (and more): Recent advances in optimization theory and methods, especially also in data science and machine learning; novel applications in technology, engineering, natural sciences, AI, etc.

#### Requirements

For Bachelor students: Nichtlineare Optimierung: Grundlagen (MA2503) recommended (not mandatory): Linear and Convex Optimization (MA2504) or (in parallel to the seminar, attendence of) Nonlinear Optimization: Advanced (MA3503). For Master students: Nichtlineare Optimierung: Grundlagen (MA2503) Nonlinear Optimization: Advanced (MA3503) recommended (not mandatory): Linear and Convex Optimization (MA2504)

#### Literature

The presentations will be based on recent journal articles.

#### Informations

In the first week of the semester we will meet (perhaps virtually) and present a selection of topics from which you can choose your preferred topic. The talks will then start 4-6 weeks later with 2 presentations per session.

#### Language

#### Number of places

#### Content

Im Zentrum der Mengenlehre steht der Unendlichkeitsbegriff und genauer das von Georg Cantor entdeckte Phänomen der Größenunterschiede im Unendlichen, das bis heute viele offene Fragen aufwirft. Weiter stellt die Mengenlehre der Mathematik eine universelle Sprache und axiomatische Grundlage zur Verfügung. Inhalt in Stichpunkten: Mengen, Mächtigkeiten, Kardinalzahlen und Ordinalzahlen, Russell-Zermelo-Antinomie, Zermelo-Fraenkel-Axiome, Auswahlaxiom, Kontinuumshypothese. Das Seminar wendet sich sowohl an Bachelor- als auch an Master-Studierende. Es können je nach Interesse und Vorwissen sowohl elementare als auch anspruchsvolle Themen vergeben werden.

#### Requirements

Mathematische Anfängervorlesungen zur Linearen Algebra und Analysis

#### Literature

Oliver Deiser: Einführung in die Mengenlehre Thomas Jech: Set Theory

#### Informations

#### Language

#### Number of places

#### Content

In jedem Kapitel des Buches "Solving Problems in Scientific Computing using Maple and Matlab" wird ein kleines Problem aus der Mathematik oder einer Anwendung vorgestellt und mithilfe einer symbolischen oder numerischen Software gelöst. Jeder Teilnehmer/in sucht sich ein Kapitel aus, trägt darüber vor und stellt ihre /seine numerischen Experimente vor.

#### Requirements

Die Inhalte der ersten drei Semester, Spaß am Programmieren.

#### Literature

Walter Gander, Jiri Hrebicek: Solving Problems in Scientific Computing using Maple and Matlab, Springer, 2004.

#### Informations

Die Auswahl der Kapitel wird noch Ende Juli stattfinden.

#### Language

#### Number of places

#### Content

As we observe in the current pandemic, stochastic effects as super-spreader events are important factors that have impact on the dynamics of an infection. We learn about stochastic models for infectious diseases, and the main tools to analyse epidemic models (Reed-Frost models, Sellke construction, Final size distribution, stochastic coupling, threshold theorems etc.)

#### Requirements

Basic knowledge about stochastics. The book is available in the library (electronically), have a look!!

#### Literature

Hakan Andersson, Tom Briton Stochastc Epidemic Models and Their Statistical Analysis Springer, 2000 F. Brauer, P. van den Driessche, J. Wu Mathemaical Epidemiology Lect. Notes in Math. 1945 Springer 2008

#### Informations

#### Language

#### Number of places

#### Content

In dem Seminar sollen stochastische Modelle auf Graphen besprochen werden. Themen sind insbesondere Perkolation, zufällige Spannbäume, Kontaktprozess, interagierende Teilchensysteme und verstärkte Irrfahrten.

#### Requirements

Probability theory (MA2409)

#### Literature

Geoffrey Grimmett: Probability on graphs: random processes on graphs and lattices. Cambridge University Press. 2010. sowie Veröffentlichungen, die auf der Seminarhomepage gelistet sind.

#### Informations

Siehe https://www-m5.ma.tum.de/Allgemeines/MA6011_2020W Es wird eine Vorbesprechung über Zoom stattfinden.

#### Language

#### Number of places

#### Content

In this seminar we will study the random cluster model and its relation to models of magnetization.

#### Requirements

Measure Theory, Probability Theory - necessary. Probability on graphs - recommended

#### Literature

"The random cluster model" by G. Grimmett. Available at https://www.statslab.cam.ac.uk/~grg/books/rcm.html

#### Informations

## Advanced seminars for Master's students

Places in the advanced seminars labeled "Master" are generally allocated to Master’s students who are already enrolled in these degree programs!

After the selection round, current Bachelor's students and external Master’s applicants can apply for any remaining places in the Master’s advanced seminars. To do so, please submit an informal application to master (at) ma.tum.de.

#### Important information for students of "Mathematics in Data Science"

The advanced seminar "Mathematics of Data Science" was specially developed for this specific degree program and is worth 5 ECTS. Should you prefer to attend an alternative advanced seminar that is usually worth only 3 ECTS, you must complete an additional requirement to earn 5 ECTS. Further, you should consult your academic advisor, PD Dr. Peter Massopust in advance, to ensure that the seminar is suited to your academic goals. After the seminar, please have the credit recognition form signed by the seminar leader and Mr. Massopust and submit it to the Infopoint of the Department of Mathematics. Credit Recognition - seminar

## Masters seminars offered during the winter semester 2020/21

#### Language

#### Number of places

#### Content

Spin glass models are archetypes for complex cost landscapes. They are discussed in a variety of applications from physics, neural networks to computer science. In this seminar you will be introduced to mean-field spin glasses as the random energy model, the Sherrington- Kirkpatrick glass and the Hopffield model for neural networks. Discussing properties of these models you will be introduced to a broad set of mathematical techniques such as concentration of measure estimates, variational methods or elements of the theory of point processes.

#### Requirements

Introduction to Probability Theory [MA1401] Probability theory [MA2409]

#### Literature

We will mostly follow Part III in: A. Bovier, Statistical mechanics of disordered systems: a mathematical perspective, Cambridge UP 2012.

#### Informations

#### Language

#### Number of places

#### Content

In this seminar, we will discover efficient and elegant algorithms for discrete optimization problems that go beyond what is taught in introductory courses. We will cover topics such as matchings in non-bipartite graphs, matroid intersection, submodular function minimization, as well as approximation algorithms for knapsack, facility location, or sparsest cut.

#### Requirements

"Algorithmische Diskrete Mathematik" or some equivalent introduction to basic algorithms

#### Literature

Korte, Vygen - Combinatorial Optimization

#### Informations

#### Language

#### Number of places

#### Content

Algebraic Geometry is an intriguing and modern subject with relations to many areas of pure mathematics such as topology, number theory, representation theory, complex geometry, but also to theoretical physics. Classically, algebraic geometry was the study of the geometry of the sets of zeroes of systems of polynomial equations. The field dramatically changed in the 60s and 70s when Grothendieck replaced the previously studied notion of algebraic varieties by his much more general notion of schemes. This new language at first seems to be more technical, and is more abstract. However, it turns out that this approach is in fact more elegant, and at the same time offers much more powerful methods. In the sequel it rapidly became the generally accepted language for this subject, and a rich theory has been developed. This course is an introduction to Algebraic Geometry. In the seminar we will review of some basic theory of algebraic varieties, introduce the spectrum of a ring, study sheaves and locally ringed spaces, and introduce schemes and some of their basic properties. We will see examples such as curves and affine and projective spaces.

#### Requirements

Algebra, Commutative Algebra

#### Literature

There are many books on the subject, for example: D. Eisenbud, J. Harris: The Geometry of Schemes U. Görtz, T. Wedhorn: Algebraic Geometry I R. Hartshorne: Algebraic Geometry D. Mumford: The red book of varieties and schemes

#### Informations

This seminar (2SWS, Bachelor and Master) is taking place twice a week in the first half of the semester. In the second half of the semester there will be a lecture (2SWS) taking place twice per week, at the same time and place as the seminar, and continuing with the subject. Exercise sessions for the lecture (2SWS) will be taking place once per week for the whole semester. In the first half we review the necessary background for the lecture (i.e. do exercises on the material of the seminar), in the second half these are "usual" exercise sessions. You can participate in the seminar, or in the lecture (including the exercise sessions), or in both, they are formally independent courses. If you want to have credit for the seminar you need to register and give a talk, if you just want the material as preparation for the lecture you can attend without registration.

#### Language

#### Number of places

#### Content

Das Seminar ist ein gemeinsamer Lektüre- und Diskussion-Kurs des Buches "Algorithms from the Book" von Kenneth Lange (SIAM, 2020). Es beschäftigt sich mit berühmten und erfolgreichen Algorithmen und ihren mathematischen Grundlagen.

#### Requirements

Solide Kenntnisse in Analysis und linearer Algebra, Grundkenntnisse in Numerik

#### Literature

Kenneth Lange, Algorithms from the Book, SIAM, 2020 (Über die Bibliothek können Sie auf eine digitale Version des Buchs im Volltext zugreifen.)

#### Informations

Weitere Informationen finden Sie unter https://www-m8.ma.tum.de/foswiki/pub/M8/Allgemeines/CarolineLasserTeach/Seminar_OscQuad_SS20.pdf?=t=12

#### Language

#### Number of places

#### Content

NP-complete optimization problems cannot be solved in polynomial time (unless P=NP). One way to obtain efficient algorithms anyway is to relax optimality. An approximation algorithm is an algorithm that runs in polynomial time and computes a feasible solution with an objective function value that is within a certain factor of that of an optimal solution. This seminar covers recent results as well as advanced techniques in the field. Participants will be assigned research papers and are expected to deliver a presentation, demonstrating in-depth understanding of the discussed problem, key technical ideas and proofs, related bibliography, and open questions.

#### Requirements

Discrete Optimization or Combinatorial Optimization

#### Literature

Original research articles.

#### Informations

TBD

#### Language

#### Number of places

#### Content

Computational Pathology encompasses algorithms and methods that answer scientific and clinical questions in pathology. In the few last years, traditional analyses are challenged with deep learning methods that allow for more standardised, robust and powerful applications. In this seminar, we will study recent research papers that develop or apply deep learning methods in a pathology context. Whenever possible, we will re-implement the applied methods, analyse the used technologies and discuss the biomedical and clinical implications.

#### Requirements

Basic knowledge of machine learning, statistics, and programming in a language like python, R or MATLAB, strong interest in biomedical Voraussetzungen and clinical applications.

#### Literature

Fuchs, T.J. & Buhmann, J.M., 2011. Computational pathology: challenges and promises for tissue analysis. Computerized medical imaging and graphics: the official journal of the Computerized Medical Imaging Society, 35(7-8), pp.515–530. Esteva, A. et al., 2017. Dermatologist-level classification of skin cancer with deep neural networks. Nature. Available at: http://www.nature.com/doifinder/10.1038/nature21056.

#### Informations

After a successful completion of the module, the students will be ableto read and evaluate scientific literature on computational pathology, and they have learned how to extract computational content and re-implement parts of the analysis. Finally, the course will strengthen the presentation and discussion skills of the participants.

#### Language

#### Number of places

#### Content

We will jointly read and discuss the classical monograph "Isolated invariant sets and the Morse index" by Charles Conley. Within roughly 80 pages, Conley develops a general global theory of dynamical systems using tools from algebraic topology. Consequently, a brief introduction to basic notions from that field will also be part of the seminar.

#### Requirements

MA 3081 Dynamical Systems

#### Literature

CONLEY, C. "Isolated Invariant Sets and the Morse Index." CBMS Lecture Notes, Providence, RI 38 (1978).

#### Informations

#### Language

#### Number of places

#### Content

The seminar will be held as a block over the course of two days (date TBA) at the Institute of Computational Biology, Helmholtz Zentrum München. Each participant has to give a talk on one of the topics below. Talks should last around 20 min. Grading will account for all aspects of the talk, in particular, whether the topic has been explained clearly and pedagogically, with the necessary level of detail. To take the most out of the seminar, we would like you to also prepare a 1-2 page summary of your topic as a handout for your fellow students so that we have an encyclopedia of advanced Deep Learning topics at the end of the seminar. You have to be registered for the exam at TUMonline.

#### Requirements

Basic machine learning knowledge, successful completion of statistical learning or introduction to deep learning is a plus

#### Literature

You can read up on these topics at https://www.deeplearningbook.org/. • Chapter 6: Deep Feedforward Networks • Chapter 8: Optimization for Training Deep Models • Chapter 9: Convolutional Networks • Chapter 10: Sequence Modeling: Recurrent and Recursive Nets

#### Informations

#### Language

#### Number of places

#### Content

The Expectation-Maximization (EM) algorithm is a popular optimization algorithm for computation of maximum likelihood estimates in statistical models for incomplete data. Examples of applications include mixture models, hidden Markov models, factor analysis and other latent variable models. The seminar participants will present classic papers introducing the EM framework and its applications, as well as recent work that gives statistical guarantees for estimates computed using EM.

#### Requirements

Probability Theory, Basic Statistics. For Master students: Computational Statistics.

#### Literature

Papers including A.P. Dempster, N.M. Laird, D.B. Rubin (1997). Maximum likelihood from incomplete data via the EM algorithm. With discussion. J. Roy. Statist. Soc. Ser. B 39(1):1-38. C. Jin, S. Balakrishnan, M.J. Wainwright, and M.I. Jordan (2016). Local maxima in the likelihood of Gaussian mixture models: Structural results and algorithmic consequences. In NIPS Conference. S. Balakrishnan, M.J. Wainwright. B. Yu (2017). Statistical guarantees for the EM algorithm: from population to sample-based analysis. Ann. Statist. 45(1): 77-120.

#### Informations

Preliminary meeting intended for early August 2020.

#### Language

#### Number of places

#### Content

Functional inequalities compare integral expressions. An elementary example is Hölder's inequality that estimates the integral of a product of two functions by a product of the integrals of appropriate powers of the individual functions. In the seminar, we prove a variety of far more sophisticated functional inequalities, for instance those that go by the names of Young, Hardy-Littlewood-Sobolev, or logarithmic Sobolev. The proofs are partially ingenious, using deep geometric constructions, hidden symmetries and non-obvious dualities. We shall also discuss applications of these inequalities in differential geometry (e.g. curvature bounds) and physics (rate of equilibration in particle systems).

#### Requirements

Participants should have completed the introductory lectures Analysis 1+2 as well as the one on measure and integration. Knowledge from the courses on functional analysis and/or PDEs are occasionally helpful, but are not needed.

#### Literature

We shall use the book E.Lieb und M.Loss: "Analysis" (GSM 14, AMS) as our main source. For more advanced talks, I can provide a plentitude of current research articles.

#### Informations

#### Language

#### Number of places

#### Content

Massive testing is an important ingredient to control infectious diseases such as the current COVID-19 pandemic. Group testing methodologies, where multiple different specimens are tested as a pool using a single test, can help increase the efficiency by reducing the number of required tests. In this seminar, we will study the extensive mathematical literature regarding the problem of determining appropriate designs of the group testing protocol. In particular, we aim to cover under which assumptions group testing makes sense at all, and if yes, which group size is optimal.

#### Requirements

MA5441 Fundamentals of Statistics

#### Literature

Ding-Zhu Du, Frank Kwang Hwang. Combinatorial Group Testing and Its Applications, World Scientific, 1993 Ding-Zhu Du, Frank Kwang Hwang. Pooling Designs And Nonadaptive Group Testing: Important Tools For Dna Sequencing, World Scientific, 2006 Matthew Aldridge, Oliver Johnson, Jonathan Scarlett. Group testing: an information theory perspective Now Publishers, 2019 Further literature for each seminar topic will be provided to the participants in the form of research articles.

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The seminar will take place in blocks on 3-5 afternoons throughout the semester.

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This seminar will provide an introduction to the theory of quantum computing, focusing on algorithms. We will cover the fundamentals of quantum mechanics and discuss known quantum algorithms and their properties. This includes Shor's algorithm, algorithms for the hidden subgroup problem, Grover's search algorithm and various related oracle-based quantum speedups.

#### Requirements

Analysis 1&2, Lineare Algebra 1&2, Einführung in die diskrete Mathematik.

#### Literature

Literature: Primarily Ronald de Wolf, Quantum Computing: Lecture Notes, arXiv:1907.09415. Additional literature TBD.

#### Informations

This seminar will be held as a block-seminar at the beginning of term. See https://www-m5.ma.tum.de/Allgemeines/Lehrveranstaltungen for additional information.

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Machine learning and uncertainty quantification (UQ) are ubiquitous in modern science and engineering applications. In the last two decades, UQ for complex physical processes has been developed rapidly with focus on grid-based process models such as finite element models which are well established in engineering applications. On the other hand, machine learning techniques have not traditionally been applied to physics-based models. The recent surge in data-driven models based on machine learning techniques such as deep learning is changing the computational science and engineering landscape. Novel hybrid models based on neural networks are emerging and are already enhancing traditional methods. In this seminar we discuss theoretical and computational aspects that arise from combining PDE-based models and neural networks, in particular, physics-informed neural networks (PINNs), neural networks for PDE approximation, and applications in UQ and turbulence models. Intended Audience: Master's students in the Faculty of Mathematics and in the Faculty of Mechanical Engineering

#### Requirements

Advanced topics in Machine Learning, Statistics, and Numerics of PDEs are covered thus we require a basic knowledge in these areas, e.g. the courses MA1401, MA3303, IN2346. Ideally, participants have prior knowledge covered in the following courses: Numerical methods for Uncertainty Quantification (MA5348) Physics-based Machine Learning (MW2450)

#### Literature

The material discussed in the seminar is based on recent research papers. Examples are: Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations https://arxiv.org/abs/1711.10561 Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations https://arxiv.org/abs/1711.10566 On the Convergence and generalization of Physics Informed Neural Networks https://arxiv.org/abs/2004.01806 Neural Operator: Graph Kernel Network for Partial Differential Equations https://arxiv.org/pdf/2003.03485.pdf Variational Physics-Informed Neural Networks For Solving Partial Differential Equations https://arxiv.org/abs/1912.00873 A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems https://arxiv.org/abs/1903.00104 A deep surrogate approach to efficient Bayesian inversion in PDE and integral equation models https://arxiv.org/abs/1910.01547 Learning and Meta-Learning of Stochastic Advection-Diffusion-Reaction Systems from Sparse Measurements https://arxiv.org/abs/1910.09098

#### Informations

Das Seminar wird zusammen mit MW (Professur Mehrskalige Modellierung von flüssigen Materialien, Prof. Zavadlav) durchgeführt. Je 5 Plätze werden für Studierende im Master Fakultät Mathematik angeboten und 5 Plätze für Master Fakultät Maschinenwesen.

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In recent years, there has been an increasing interest in topics at the intersection of economics and computer science, as witnessed by the continued rapid rise of research areas such as algorithmic game theory and computational social choice. This development is due to the emergence of computational networks such as the Internet as well as the need to get a grip on algorithmic questions in economics. In this seminar, we will deal with both the theoretical foundations as well as their computational properties and possible applications.

#### Requirements

It is expected that participants are experienced in formally proving mathematical statements and are familiar with standard proof techniques. Additionally, basic knowledge of complexity theory is useful (e.g., module IN0011).

#### Literature

The seminar will mostly be based on the books Economics and Computation by David C. Parkes and Sven Seuken and the Handbook of Computational Social Choice. Both books will be available for free download for participants of the seminar in our Moodle course http://go.tum.de/612829 via the guest key provided during the seminar overview meeting.

#### Informations

There will be a seminar overview (Vorbesprechung) online meeting on Friday, July 10, 2020. All students have to apply for the seminar. Further information (including the application procedure) can be found in the course homepage: go.tum.de/291400

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Not only in times of COVID-19, communicable diseases were big threats to populations. A better, quantitative understanding of these processes help also to develop defense strategies or how to optimise treatments. Different mathematical tools may be appropriate as modelling approaches. In the seminar, we will mainly focus on Ordinary differential equations and Partial differential equations Often, the dynamic behaviour for whole populations is described by differential equation models. PDEs allow e.g. for considering spatial models. For small populations, stochastic models may be more appropriate. We will discuss typical modelling approaches including their analysis as well as concrete examples for diseases (like Influenza, HIV, and Tuberculosis). This seminar will be based on parts of the book “Mathematical Models for Communicable Diseases” by Fred Brauer and Carlos Castillo-Chavez and further original papers in this context dependent on the interests and previous knowledge of the participants.

#### Requirements

Mathematical models in Biology, Knowledge in Ordinary differential equations

#### Literature

Fred Brauer, Carlos Castillo-Chavez: Mathematical Models for Communicable Diseases, SIAM 2013 and other publications in this context

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Further organisation, e.g. choice of preferred topic for the talk etc. will be done after the group of participants is fixed. Questions are always welcome!

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1. “Deep learning” (T+P) 2. “Identification of neural networks 1” (T) 3. “Identification of neural networks 2” (T+P) 4. “Approximation theory” of neural networks (T) 5. ”Reinforcement Learning” (T+P) 6. “Stochastic gradient descent” (T+P 7. “Consensus based optimization” (T+P) 8. “Johnson-Lindenstrauss Lemma + Clustering (k-means etc.)” (T+P) 9. “Compressed sensing” (T+P) 10. “Johnson-Lindenstrauss Lemma + Restricted Isometry property”(T) 11. “Learning with kernels and SVM” (T+P)

#### Requirements

Linear Algebra Probability Convex Optimization Foundations of Data Analysis

#### Literature

http://www.deeplearningbook.org/ http://www.ems-ph.org/journals/show_pdf.php?issn=0213-2230&vol=10&iss=3&rank=2 https://arxiv.org/pdf/1804.01592 & https://arxiv.org/pdf/1907.00485 https://arxiv.org/pdf/1901.02220 http://rail.eecs.berkeley.edu/deeprlcourse-fa17/index.html http://papers.nips.cc/paper/5355-stochastic-gradient-descent-weighted-sampling-and-the-randomized-kaczmarz-algorithm.pdf https://arxiv.org/pdf/1909.09249 https://arxiv.org/pdf/2003.05086 https://arxiv.org/pdf/2001.11988 http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.141.4812&rep=rep1&type=pdf https://arxiv.org/pdf/1408.4045.pdf https://people.ricam.oeaw.ac.at/m.fornasier/CSFornasierRauhut.pdf (T+P) https://link.springer.com/content/pdf/10.1007/s00365-007-9003-x.pdf https://arxiv.org/pdf/1009.0744.pdf https://stuff.mit.edu/afs/athena/course/9/9.s915/OldFiles/www/classes/dealing_with_data.pdf https://www.cs.utah.edu/~piyush/teaching/learning-with-kernels.pdf

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We consider optimal control problems governed by partial differential equations (PDEs) and discretize them using finite elment methods (FEM). For resulting discretization we discuss a priori and a posteriori error estimates as well as adaptive strategies for solution.

#### Requirements

Modern Methods in Nonlinear Optimization (MA4503)

#### Literature

Aktuelle Forschungsartikel, die in der Vorbesprechung bekannt gegeben werden.

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Dieses Seminar widmet sich aktuelle Entwicklungen der nichtlinearen Optimierung und bereitet zudem auf eine Bachelor- oder Masterarbeit in diesem Gebiet vor. In den Vorträgen werden insbesondere aktuelle Themen aus folgenden Bereichen der nichtlinearen Optimierung behandelt: Neue Entwicklungen in Theorie und Methoden der Optimierung, speziell auch in den Bereichen Data Science und Machine Learning; innovative Anwendungen in Technik, Natur- und Wirtschaftswissenschaften, KI, etc. English version: This seminar addresses recent advances in nonlinear optimization and also serves as a preparation for a Bachelor's or Master's thesis in this field. The seminar covers the following topics (and more): Recent advances in optimization theory and methods, especially also in data science and machine learning; novel applications in technology, engineering, natural sciences, AI, etc.

#### Requirements

For Bachelor students: Nichtlineare Optimierung: Grundlagen (MA2503) recommended (not mandatory): Linear and Convex Optimization (MA2504) or (in parallel to the seminar, attendence of) Nonlinear Optimization: Advanced (MA3503). For Master students: Nichtlineare Optimierung: Grundlagen (MA2503) Nonlinear Optimization: Advanced (MA3503) recommended (not mandatory): Linear and Convex Optimization (MA2504)

#### Literature

The presentations will be based on recent journal articles.

#### Informations

In the first week of the semester we will meet (perhaps virtually) and present a selection of topics from which you can choose your preferred topic. The talks will then start 4-6 weeks later with 2 presentations per session.

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Im Zentrum der Mengenlehre steht der Unendlichkeitsbegriff und genauer das von Georg Cantor entdeckte Phänomen der Größenunterschiede im Unendlichen, das bis heute viele offene Fragen aufwirft. Weiter stellt die Mengenlehre der Mathematik eine universelle Sprache und axiomatische Grundlage zur Verfügung. Inhalt in Stichpunkten: Mengen, Mächtigkeiten, Kardinalzahlen und Ordinalzahlen, Russell-Zermelo-Antinomie, Zermelo-Fraenkel-Axiome, Auswahlaxiom, Kontinuumshypothese. Das Seminar wendet sich sowohl an Bachelor- als auch an Master-Studierende. Es können je nach Interesse und Vorwissen sowohl elementare als auch anspruchsvolle Themen vergeben werden.

#### Requirements

Mathematische Anfängervorlesungen zur Linearen Algebra und Analysis

#### Literature

Oliver Deiser: Einführung in die Mengenlehre Thomas Jech: Set Theory

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In response to the challenges of COVID-19, this seminar will train students in spatio-temporal modeling for analysis and prediction of the epidemiology of infectious diseases worldwide. Students will select a leading statistical methods paper in the field to present, and have the choice of extended research in the area of the paper versus their own visualization and analysis of web-scraped real-time COVID data. Interested students who can meet the requirements should send the following items from a TUM email address to Prof. Donna Ankerst at ankerst@tum.de no later than July 19, 2020: • Transcript of TUM Master grades, • Email text statement of motivation for the seminar, including selection of 3 papers from Literature in order of priority with motivation.

#### Requirements

Participation in applied regression, generalized linear models, multivariate statistics, and/or computational statistics

#### Literature

1) Sansom P, Copley VR, Naik FC, Leach S, Hall IM. A case-association cluster detection and visualisation tool with an application to Legionnaires' disease. Stat Med.2013;32(20):3522-3538. doi:10.1002/sim.5765 2) Diggle PJ, Moraga P, Rowlingson B, Taylor BM. Spatial and spatio-temporal log-Gaussian Cox processes: extending the geostatistical paradigm. Statistical Science. 2013;28(4):542-563. doi:10.1214/13-STS441 3) Malesios C, Demiris N, Kalogeropoulos K, Ntzoufras I. Bayesian epidemic models for spatially aggregated count data. Stat Med. 2017;36(20):3216-3230. doi:10.1002/sim.7364 4) Meyer S, Held L. Power-law models for infectious disease spread. Annals of Applied Statistics. 2014;8(3):1612-1639. doi:10.1214/14-AOAS743 5) Paul M, Held L, Toschke AM. Multivariate modelling of infectious disease surveillance data. Stat Med. 2008;27(29):6250-6267. doi:10.1002/sim.3440 6) Stocks T, Britton T, Höhle M. Model selection and parameter estimation for dynamic epidemic models via iterated filtering: application to rotavirus in Germany. Biostatistics. 2020;21(3):400-416. doi:10.1093/biostatistics/kxy057 7) Diggle PJ. Spatio-temporal point processes, partial likelihood, foot and mouth disease. Stat Methods Med Res. 2006;15(4):325-336. doi:10.1191/0962280206sm454oa 8) Heaton MJ, Berrett C, Pugh S, Evans A, Sloan C. Modeling bronchiolitis incidence proportions in the presence of spatio-temporal uncertainty. Journal of the American Statistical Association. 2020;115(529):66-78. doi:10.1080/01621459.2019.1609480 9) Hazelton ML. Testing for changes in spatial relative risk. Stat Med. 2017;36(17):2735-2749. doi:10.1002/sim.7306 10) Lowe R, Bailey TC, Stephenson DB, et al. The development of an early warning system for climate-sensitive disease risk with a focus on dengue epidemics in Southeast Brazil. Stat Med. 2013;32(5):864-883. doi:10.1002/sim.5549 11) Lin PS, Zhu J. A heterogeneity measure for cluster identification with application to disease mapping. Biometrics. 2020;76(2):403-413. doi:10.1111/biom.13145 12) Mahsin MD, Deardon R, Brown P. Geographically dependent individual-level models for infectious diseases transmission [published online ahead of print, 2020 Mar 2]. Biostatistics. 2020;kxaa009. doi:10.1093/biostatistics/kxaa009 13) Meyer S, Held L. Incorporating social contact data in spatio-temporal models for infectious disease spread. Biostatistics. 2017;18(2):338-351. doi:10.1093/biostatistics/kxw051 14) Held L, Meyer S, Bracher J. Probabilistic forecasting in infectious disease epidemiology: the 13th Armitage lecture. Stat Med. 2017;36(22):3443-3460. doi:10.1002/sim.7363

#### Informations

Thursdays 2-4 pm, virtual attendance mandatory

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A proper q-coloring of a graph is an assignment of one of q colors to each vertex of the graph so that adjacent vertices are colored differently. Sample uniformly among all proper q-colorings of a large discrete cube in the d-dimensional integer lattice. Does the random coloring obtained exhibit any large-scale structure? Does it have fast decay of correlations? We discuss these questions and the way their answers depend on the dimensiondd and the number of colors q. The questions are motivated by statistical physics (anti-ferromagnetic materials, square ice) and combinatorics (proper colorings, independent sets) .

#### Requirements

Probability Theory (notwendig) Markov Processes (empfohlen)

#### Literature

Ron Peled, Yinon Spinka: Three lectures on random proper colorings of Z^d (available at https://arxiv.org/abs/2001.11566 Sasha Friedli, Yvan Velenik: Statistical Mechanics of Lattice Systems: a Concrete Mathematical Introduction (availbale from the homepage of the second author)

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You should know probability theory - knowledge in physics is not necessary to follow the seminar.

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As we observe in the current pandemic, stochastic effects as super-spreader events are important factors that have impact on the dynamics of an infection. We learn about stochastic models for infectious diseases, and the main tools to analyse epidemic models (Reed-Frost models, Sellke construction, Final size distribution, stochastic coupling, threshold theorems etc.)

#### Requirements

Basic knowledge about stochastics. The book is available in the library (electronically), have a look!!

#### Literature

Hakan Andersson, Tom Briton Stochastc Epidemic Models and Their Statistical Analysis Springer, 2000 F. Brauer, P. van den Driessche, J. Wu Mathemaical Epidemiology Lect. Notes in Math. 1945 Springer 2008

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In dem Seminar sollen stochastische Modelle auf Graphen besprochen werden. Themen sind insbesondere Perkolation, zufällige Spannbäume, Kontaktprozess, interagierende Teilchensysteme und verstärkte Irrfahrten.

#### Requirements

Probability theory (MA2409)

#### Literature

Geoffrey Grimmett: Probability on graphs: random processes on graphs and lattices. Cambridge University Press. 2010. sowie Veröffentlichungen, die auf der Seminarhomepage gelistet sind.

#### Informations

Siehe https://www-m5.ma.tum.de/Allgemeines/MA6011_2020W Es wird eine Vorbesprechung über Zoom stattfinden.

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In this seminar we will study the random cluster model and its relation to models of magnetization.

#### Requirements

Measure Theory, Probability Theory - necessary. Probability on graphs - recommended

#### Literature

"The random cluster model" by G. Grimmett. Available at https://www.statslab.cam.ac.uk/~grg/books/rcm.html

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Diffusion (of particle systems, say) is a ubiquitous process in nature. How can we describe diffusion processes and more generally statistical phenomena on a macroscopic scale, as evolution of a density? We will study several approaches, including Markov semigroups, Frobenius-Perron operators and Koopman operators. The framework will reveal beautiful connections to geometry and physics, notably the entropy. One aim of this seminar is to explore these connections a bit. The seminar will run as online seminar jointly between TUM and Imperial College London.

#### Requirements

Analysis and/or probability. The seminar will cover both analytic and probabilistic topics, so an interest in these fields is important. The talks will be tailored to the individual background.

#### Literature

Dominique Bakry, Ivan Gentil und Michel Ledoux: Analysis and geometry of Markov diffusion operators, Springer 2014 Andrzej Lasota und Michael C. Mackey: Chaos, fractals, and noise, Springer 1994.

#### Informations

Students interested in participating are kindly asked to contact the organisers directly by email until 30 July 2020, so we can arrange an information/preparation session. The organisers are Johannes Zimmer (ne52yap@mytum.de, TUM) and Greg Pavliotis (g.pavliotis@imperial.ac.uk, Imperial).