# Seminars and workshops

## Dates for seminars in the winter semester 2021/22

Registration for seminars for the winter semester 2021/22 will take place via the matching system again.

Seminars that are suitable for students of the TUM School of Education contain a corresponding note in the seminar description.

1 July 2021: Program announced for winter semester 2021/22

5 July (12:00) - 12 July 2021 (12:00): Students register using the matching system

14 July - 21 July 2021: Lecturer's selection round

26 July 2021: results are available in the matching system

## 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. Shortly before the start of the semester you will be registered for the exam and can then see the registration in TUMonline under your "registered examinations".

If you were not allocated a place in the matching or if you would like to take part in a second seminar, please ask the respective lecturers of a seminar with remaining places, if you may take part. If they agree please email bachelor (at) ma.tum.de or master (at) ma.tum.de and cc the seminar’s lecturer to be registered for the Bachelor's or Master's seminar.

## 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. Please contact the respective seminar lecturer to apply for one of the remaining places. If he/she agrees, please send an email to master (at) ma.tum.de and cc the seminar's lecturer to be registered for the Master's seminar.

## Bachelor's seminars offered in the winter semester 2021/22

#### Language

#### Number of places

#### Content

Das Seminar ist ein gemeinsamer Lektüre- und Diskussionskurs des Buches "Algorithms from the Book" von Kenneth Lange (SIAM, 2020). Es beschäftigt sich mit berühmten und erfolgreichen Algorithmen und ihren mathematischen Grundlagen. Kenneth Lange arbeitet derzeit an einer Neuauflage des Buches. Wir werden neue Kapitel zur preview benutzen dürfen.

#### Requirements

Solide Kenntnisse in Analysis, linearer Algebra und Numerik.

#### Literature

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

#### Informations

#### Language

#### Number of places

#### Content

Functional inequalities provide a method to compare functions to each other in view of certain features. How symmetric is a function under certain operations? How wiggly is it? How close is it to a given set functions? Such questions play an important role in mathematical physics, differential geometry, PDE analysis and many more fields, and functional inequalities give an answer in terms of robust integral expression. In this seminar, we shall encounter several well-known functional inequalities, like rearrangement, Hardy-Littlewood-Sobolev, logarithmic Sobolev and Hausdorff-Young inequalities. The proofs will provide information on the optimal constants and the optimizers, which achieve equality. In each case, the method of proof rests on some deep insight and has an inherent beauty. Applications, for instance to the estimate on the rates of equilibration in particle systems or to bound the Ricci curvature of manifolds, will be discussed depending on the interest of the participants.

#### Requirements

Analysis, LADS and Maßtheorie are a must. Basic knowledge in functional analysis and/or PDEs is helpful for some topics, but is not at all necessary to enjoy the seminar.

#### Literature

For the specific functional inequalities mentioned above, we follow E.Lieb und M.Loss: "Analysis" (GSM 14, AMS). For further inequalities and the mentioned applications, additional material will be provided.

#### 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

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

Experience in formally proving mathematical statements (standard proof techniques) Basic knowledge of complexity theory is useful (e.g., module IN0011)

#### Literature

David C. Parkes and Sven Seuken: "Economics and Computation" (guest key published during overview meeting) Brandt et al.: "Handbook of Computational Social Choice" (freely available as PDF)

#### Informations

All students have to apply for the seminar. Further information (including the application procedure) can be found on the course homepage: https://dss.in.tum.de/teaching/ws-21-22/49-teaching/semester/winter-semester-2021-22/256-seminar-on-markets-algorithms-incentives-and-networks-ws21-22.html Please attend the overview meeting if you are interested in participating.

#### Language

#### Number of places

#### Content

Can we estimate the time when humanity did leave Africa? Can we obtain, from genetic data only, size and history of a population? Population genetics allows to answer such questions, purely in looking into the signature of mutations. In this seminar, we will start with a review of the basis of population genetics (Kingman coalescent, measures for genetic diversity, site-frequency spectrum) to proceed thereafter to more advanced mathematical models that allow to analyze the evolution of so far neglected biological systems with generation overlap (bacteria, viruses, seeds of plants but also trees or long lived mammals). In the seminar course we aim to discuss the existing literature in this area with the objective of developing better suited mathematical models.

#### Requirements

Basic stochastics.

#### Literature

Durrett, R. (2008). Probability Models for DNA Sequence Evolution (Springer). Original papers for the more specialized talks.

#### Informations

Falls ein Termin Freitags 14:00 möglich wäre, so würden wir das begrüßen.

#### Language

#### Number of places

#### Content

Viele Probleme der Statistik können in algebraischer Sprache beschrieben werden und lassen sich deshalb mittels algebraischer Methoden lösen. Dieses Seminar bietet eine Einführung in die Welt der algebraischen Statistik. Am Anfang des Seminars präsentieren wir alle notwendige algebraische Begriffe, wie z.B. Polynome, Ideale und Gröbner-Basen. Parallel dazu lernen wir den Umgang mit Computeralgebrasystemen. Anschließend sehen wir ausgewählte Anwendungen in der Statistik, wie zum Beispiel Unabhängigkeit in Graphischen Modellen und Markow-Basen für Hierarchische Modelle.

#### Requirements

Einführung in die Wahrscheinlichkeitstheorie und Statistik.

#### Literature

Wir betrachten ausgewählte Kapitel der folgenden Bücher: Cox D, Little J, and O'Shea D. 2007. Ideals, Varieties and Algorithms. Undergraduate Texts in Mathematics. Springer-Verlag. Sullivant S. 2018. Algebraic Statistics. Graduate Studies in Mathematics. American Mathematical Society.

#### Informations

Eine Vorbesprechung findet Anfang Oktober statt. Vorträge können in deutscher oder englischer Sprache gehalten werden.

#### Language

#### Number of places

#### Content

Chains of infinite order, first introduced by Doblin and Fortet in 1937, are the generalization of k-step Markov chains when the parameter k approaches infinity. The study of those chains is of significance in a variety of fields, such as Probability Theory, Statistical Mechanics and Ergodic Theory. For further information, please visit the seminar's website https://www-m5.ma.tum.de/Allgemeines/CIO_2021W

#### Requirements

Introduction to Probability and Statistics, Markov Chains, Measure Theory

#### Literature

We will read several old and new papers together. Please visit the website of the seminar https://www-m5.ma.tum.de/Allgemeines/CIO_2021W for a list of those papers.

#### Informations

#### Language

#### Number of places

#### Content

Measure concentration deals with the general fact that reasonable functions on large probability spaces typically take on values close to the average. This seminar provides an introduction to some of the existing techniques for establishing such results. Connections and applications to various geometric inequalities and some applications will also be discussed.

#### Requirements

Probability theory, measure- and integration theory

#### Literature

Primarily: M. Ledoux, The Concentration of Measure Phenomenon, AMS, 2001. Additional literature: TBA.

#### Informations

see http://www-m5.ma.tum.de/Allgemeines/Lehrveranstaltungen

#### Language

#### Number of places

#### Content

Linear algebraic groups are an important class of groups that come with the structure of an algebraic variety. Examples include the general linear group, the special linear group or the orthogonal group over a field. In this seminar, we will develop the foundations of the theory of linear algebraic groups. We will discuss the basic definitions, important subgroups such as tori and Borel subgroups, the relationship between a linear algebraic group and its Lie algebra, as well as the root datum of a linear algebraic group. The endpoint of the seminar will be a discussion of the classification of reductive groups. The most important tools for our course come from linear algebra and algebraic geometry. The necessary prerequisites from algebraic geometry will be explained in the seminar, with the level of detail depending on the participants' backgrounds. The theory of linear algebraic groups has a number of applications in algebraic geometry, finite group theory and many other subjects. Moreover, while the foundations are well-understood and accessible, open questions related to linear algebraic groups are ubiquitous in modern mathematical research.

#### Requirements

Commutative Algebra within the scope of Algebra 2 Experience with algebraic geometry is very helpful, but not required

#### Literature

T.A. Springer . Linear Algebraic Groups J.E. Humphreys. Linear Algebraic Groups R. Carter, G. Segal, I. Macdonald. Lectures on Lie Groups and Lie Algebras

#### Informations

#### Language

#### Number of places

#### Content

The idea of Mathematical Epidemiology is to understand the spread of diseases, to make forcast about the progression of diseases and to understand possible effects of interventions. In this seminar, we will consider typical model approaches and their analysis in this area. Starting with basic epidemic model, we will include more and more structure behind, also concerning demography. Another important problem are so-called vector-borne diseases (like Malaria) and their treatments. One aspect of the seminar will be also the consideration of data, how to extract important information and how to make reliable predictions. Different mathematical tools may be appropriate and used as modelling approaches, e.g. Ordinary differential equations, Delay differential equations and Partial differential equations, but also some statistical techniques.

#### Requirements

Mathematical models in Biology, Knowledge in Ordinary differential equations

#### Literature

This seminar will be based on parts of the book “An Introduction to Mathematical Epidemiology” by Maia Martcheva and further original papers in this context dependent on the interests and previous knowledge of the participants.

#### Informations

Further organisation, e.g. choice of preferred topic for the talk etc. will be done after the group of participants is fixed. If there are special interests, please contact me as soon as possible. Questions are always welcome, also in advance!

#### Language

#### Number of places

#### Content

Die Fortschritte in 3d Rendering und as Aufkommen von 3D Druckverfahren eröffnet der mathematischen Visualisierung neue Möglichkeiten. Veranschaulichungen mathematischen Sachverhalte und Objekte können relativ einfach visualisiert und physisch realisiert werden. In diesem Seminar sollen die Studenten in kleinen Gruppen ein oder mehrere mathematische Modelle erstellen. Bei dem Modell kann es sich um eine Fläche, wie die Kuen'sche Fläche, einen Körper - wie das Oloid oder aber einen Sachverhalt - wie die Spur eines Brennpunktes einer Ellipse unter Abrollen oder die Vercknickbarkeit spezieller Vierecksnetze - handeln. Die Studenten sollen die Objekte verstehen, die nötigen Daten generieren und soweit aufbereiten, dass am Ende eine Visualisierung erstellt und/oder ein 3D Modell gedruckt werden kann. Dieses Modell soll dann im Vortrag vorgestellt und erklärt werden. Einige Beispiele können hier gesehen werden: https://www- m10.ma.tum.de/bin/view/Lehre/WS1415/ModelleSeminar Die zur Erstellung und Aufbereitung der Modelle nötigen Softwaresysteme werden im Seminar besprochen.

#### Requirements

Analysis und Lineare Algebra. Differentialgeometrie: Grundlagen und/oder Geometriekalküle bz. Geometrie, ein wenig Programmiererfahrung (wie z.B. python, java, Julia, c, etc...).

#### Literature

Je nach zu bearbeitendem Modell passende Fachartikel.

#### Informations

Die Abhaltung (in Person, online, eine Mischung...) wird sich den Gegebenheiten im kommenden Wintersemester anpassen (müssen).

#### Language

#### Number of places

#### Content

Das Seminar soll sich mit der mathematischen Modellierung biologischer Vorgänge im menschlischen Körper befassen. Behandelt werden dabei sowohl zelluläre Prozesse, wie auch die Funktion ganzer Organe. Typischerweise führt dies auf (nichtlineare) Differentialgleichungen, die anschließend durch geeignete Näherungsmethoden oder numerisch gelöst werden können.

#### Requirements

Interesse an Biologie, Chemie, mathematischer Modellierung und Differentialgleichungen.

#### Literature

James Keener, James Sneyd: Mathematical Physiology, I: Cellular Physiology, Springer Verlag, New York, 2008. James Keener, James Sneyd: Mathematical Physiology, II: Systems Physiology, Springer Verlag, New York, 2008.

#### Informations

Voraussichtlicher Termin: Do 14-16 Uhr

#### Language

#### Number of places

#### Content

This seminar introduces the students to the analysis of actuarial mortality data to fit mathematical models used in the valuation of insurance and pension portfolios. It covers the mathematical analysis of regression models, defines the concept of force of mortality (hazard rate) and introduce some parametric models widely used by practitioners. The lecturers will show the application of these models to the analysis of actuarial datasets and of Human Mortality Data, and their use in pricing basic life insurance contract (e.g. annuities).

#### Requirements

MA0009

#### Literature

A. S. Macdonald, S. J. Richards, and I, D. Currie (2018). Modelling Mortality with Actuarial Applications

#### Informations

The preliminary online-meeting to the Seminar (Online-Seminarvorbesprechung) will take place on July 8th, 2021 at 17:00 in ZOOM. Please write an e-mail to min@tum.de to get an access to this ZOOM-meeting.

#### Language

#### Number of places

#### Content

Random graphs are used as probabilistic models for complex networks. In the seminar we want to study several well know random graph models including the Erdös-Renyi random graph and the preferential attachment model. In particular, we will study the phase transition for the Erdös-Renyi random graph. During the seminar, we will learn important tools in the study of stochastic processes including couplings, stochastic order, probabilistic bounds and branching processes.

#### Requirements

Einführung in die Wahrscheinlichkeitstheorie und Statistik (MA0009) oder Einführung in die Wahrscheinlichkeitstheorie MA1401

#### Literature

R. van der Hofstad. Random Graphs and Complex Networks. Volume 1. Cambridge Series in Statistical and Probabilistic Mathematics (2017)

#### Informations

https://www-m5.ma.tum.de/Allgemeines/MA6011_2021W Es wird eine Vorbesprechung über Zoom stattfinden, bei der die Vortragsthemen verteilt werden.

#### Language

#### Number of places

#### Content

Topologische Räume Stetigkeit Zusammenhang Kompaktheit Dimension Metrisierbarkeitssätze Polnische Räume Themen der deskriptiven Mengenlehre (Borel-Mengen, projektive Mengen, Determiniertheit) Topological Spaces Continuity Connected Spaces Compact Spaces Dimension Metrization Theorems Polish Spaces Selected Topics in Descriptive Set Theory (Borel sets, projective sets, Determinacy)

#### Requirements

Mathematische Grundvorlesungen

#### Literature

Sieradski: Topology and Homotopy Dugundji: Topology Kechris: Classical Descriptive Set Theory

#### 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. Please contact the respective seminar lecturer to apply for one of the remaining places. If he/she agrees, please send an email to master (at) ma.tum.de and cc the seminar's lecturer to be registered for the Master's seminar.

#### 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 2021/22

#### Language

#### Number of places

#### Content

Fair division problems ask the fundamental question of how to allocate resources to agents fairly. The mathematical problems studied depend on the concrete context (e.g., divisible or indivisible resources) and various fairness criteria (e.g., envy-freeness, proportionality, maximin share). Here is a simple example: Imagine a cake that two people want to share fairly. Each has their own, private valuation function on the points of the cake. Is there a protocol they can use to divide the cake so that no person envies the piece of the other, but also no one has to reveal their valuation function? There is, and it is quite easy: (any) one person cuts two pieces, and the other person picks their favorite. Therefore, it is in the best interest of the cutter to cut two pieces of equal value for themselves and be happy with whatever piece the other person chooses. Quite impressively, this protocol is described in ancient scripts (Theogony and Bible), which were written at least 2700 years ago! Even though simple to state, abstractions of these problems can capture the essence of important real-life applications from political science and microeconomics to computer science and operations research. A great line of works has studied the conditions under which a desired fair solution always exists (or does not) and the algorithmic complexity required to achieve (near) optimum solutions. In this seminar, we will glance at some of the most-studied fair division problems of the last decades, meet colorful ideas to attack them, and understand their algorithmic and optimization aspects. The original papers we will study involve techniques from algebraic topology, optimization, or approximation algorithms.

#### Requirements

Mathematical maturity and curiosity.

#### Literature

Original articles

#### Informations

TBD

#### Language

#### Number of places

#### Content

We will have a closer look at Gaussian processes and related methods in light of their applications for machine learning.

#### Requirements

Basic knowledge of probability theory and statistics is required. Knowledge of machine learning basics would be useful.

#### Literature

Main literature: Carl Edward Rasmussen, Christopher K.I. Williams „Gaussian Processes for Machine Learning“ (MIT Press 2006); available at http://www.gaussianprocess.org/ Further literature will be provided in due time.

#### 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

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

Experience in formally proving mathematical statements (standard proof techniques) Basic knowledge of complexity theory is useful (e.g., module IN0011)

#### Literature

David C. Parkes and Sven Seuken: "Economics and Computation" (guest key published during overview meeting) Brandt et al.: "Handbook of Computational Social Choice" (freely available as PDF)

#### Informations

All students have to apply for the seminar. Further information (including the application procedure) can be found on the course homepage: https://dss.in.tum.de/teaching/ws-21-22/49-teaching/semester/winter-semester-2021-22/256-seminar-on-markets-algorithms-incentives-and-networks-ws21-22.html Please attend the overview meeting if you are interested in participating.

#### Language

#### Number of places

#### Content

The idea of Mathematical Epidemiology is to understand the spread of diseases, to make forcast about the progression of diseases and to understand possible effects of interventions. In this seminar, we will consider typical model approaches and their analysis in this area. Starting with basic epidemic model, we will include more and more structure behind, also concerning demography. Another important problem are so-called vector-borne diseases (like Malaria) and their treatments. One aspect of the seminar will be also the consideration of data, how to extract important information and how to make reliable predictions. Different mathematical tools may be appropriate and used as modelling approaches, e.g. Ordinary differential equations, Delay differential equations and Partial differential equations, but also some statistical techniques.

#### Requirements

Mathematical models in Biology, Knowledge in Ordinary differential equations

#### Literature

This seminar will be based on parts of the book “An Introduction to Mathematical Epidemiology” by Maia Martcheva and further original papers in this context dependent on the interests and previous knowledge of the participants.

#### Informations

Further organisation, e.g. choice of preferred topic for the talk etc. will be done after the group of participants is fixed. If there are special interests, please contact me as soon as possible. Questions are always welcome, also in advance!

#### Language

#### Number of places

#### Content

Das Seminar soll sich mit der mathematischen Modellierung biologischer Vorgänge im menschlischen Körper befassen. Behandelt werden dabei sowohl zelluläre Prozesse, wie auch die Funktion ganzer Organe. Typischerweise führt dies auf (nichtlineare) Differentialgleichungen, die anschließend durch geeignete Näherungsmethoden oder numerisch gelöst werden können.

#### Requirements

Interesse an Biologie, Chemie, mathematischer Modellierung und Differentialgleichungen.

#### Literature

James Keener, James Sneyd: Mathematical Physiology, I: Cellular Physiology, Springer Verlag, New York, 2008. James Keener, James Sneyd: Mathematical Physiology, II: Systems Physiology, Springer Verlag, New York, 2008.

#### Informations

Voraussichtlicher Termin: Do 14-16 Uhr

#### Language

#### Number of places

#### Content

Can we estimate the time when humanity did leave Africa? Can we obtain, from genetic data only, size and history of a population? Population genetics allows to answer such questions, purely in looking into the signature of mutations. In this seminar, we will start with a review of the basis of population genetics (Kingman coalescent, measures for genetic diversity, site-frequency spectrum) to proceed thereafter to more advanced mathematical models that allow to analyze the evolution of so far neglected biological systems with generation overlap (bacteria, viruses, seeds of plants but also trees or long lived mammals). In the seminar course we aim to discuss the existing literature in this area with the objective of developing better suited mathematical models.

#### Requirements

Basic stochastics.

#### Literature

Durrett, R. (2008). Probability Models for DNA Sequence Evolution (Springer). Original papers for the more specialized talks.

#### Informations

Falls ein Termin Freitags 14:00 möglich wäre, so würden wir das begrüßen.

#### Language

#### Number of places

#### Content

This seminar is particularly tailored to the students of the Master of "Mathematics in Data Science" in order to offer them 5 ECTS. The seminar explores relevant contributions of mathematics in data science. We consider both theoretical (T) and practical/algorithmic (P) aspects. The topics include “Deep learning” (T+P) “Identification of neural networks 1” “Identification of neural networks 2” “Approximation theory” of neural networks (T) ”Reinforcement Learning” (T+P) “Stochastic gradient descent” (T+P) “Optimization for deep learning” (T+P) “Consensus based optimization” (T+P) “Johnson-Lindenstrauss Lemma + Clustering (k-means etc.)” (T+P) “Compressed sensing” (T+P) “Johnson-Lindenstrauss Lemma and Restricted Isometry property” (T) “Learning with kernels and Support Vector Machines” (T+P)

#### Requirements

The prerequisite of the seminar are the basics of Linear Algebra, Analysis, Optimization, Probability and the seminar is particularly tailored to student who already attended the course Foundations of Data Analysis

#### Literature

The seminar will be based on book chapters and research papers, which are available online: http://www.deeplearningbook.org/ http://www.ems-ph.org/journals/show_pdf.php?issn=0213-2230&vol=10&iss=3&rank=2 https://www.mins.ee.ethz.ch/pubs/files/nn-id-2019.pdf 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/1912.08957.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://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

#### Informations

#### Language

#### Number of places

#### Content

The seminar will give an introduction to nonlinear methods for statistical inference of cause-effect relationships in multivariate data. The considered methodology builds on structural causal models that not only model stochastic dependencies among the observed variables but also make predictions about the effects of external interventions. In this context, non-linear relationships among the variables may help to reveal detailed causal relations. When applying for participation, please send a TUM grade transcript to david.strieder@tum.de.

#### Requirements

Basic statistics and probability + a Master level statistics course.

#### Literature

We will consider selected papers from the literature such as: Peters, Jonas; Mooij, Joris M.; Janzing, Dominik; Schölkopf, Bernhard: Causal discovery with continuous additive noise models. J. Mach. Learn. Res. 15 (2014), 2009–2053. Zhang, Kun; Hyvarinen, Aapo: On the Identifiability of the Post-Nonlinear Causal Model. https://arxiv.org/abs/1205.2599 Zhang, Kun; Hyvärinen, Aapo: Nonlinear functional causal models for distinguishing cause from effect. Statistics and causality, 185–201, Wiley Ser. Probab. Stat., Wiley, Hoboken, NJ, 2016. 62J02 (62A01 62B10) Bühlmann, Peter; Peters, Jonas; Ernest, Jan: CAM: causal additive models, high-dimensional order search and penalized regression. Ann. Statist. 42 (2014), no. 6, 2526–2556. Rothenhäusler, Dominik; Ernest, Jan; Bühlmann, Peter Causal: inference in partially linear structural equation models. Ann. Statist. 46 (2018), no. 6A, 2904–2938. 62G99 (62H99 68T99) Agrawal, Raj; Squires, Chandler; Prasad, Neha; Uhler, Caroline: The DeCAMFounder: Non-Linear Causal Discovery in the Presence of Hidden Variables. https://arxiv.org/abs/2102.07921

#### Informations

Preliminary meeting in September 2021.

#### Language

#### Number of places

#### Content

In this seminar we discuss both theoretical issues and numerical analysis for carefully chosen optimal control problems with PDEs. The topics are based on current research literature and can build a basis for master theses.

#### Requirements

Numerical Methods for PDEs

#### Literature

to be announced

#### Informations

#### Language

#### Number of places

#### Content

We study probabilistic models for the evolutions of opinions under some exchange dynamics. Agents hold opinions (for instance an opinion can be an element of [0,1]) and will adjust to each other, following certain rules. How does the system evolve over time? Such models are widespread in economics and there are many challenges and open problems for probability theory.

#### Requirements

Probability Theory (compulsory) Markov processes (recommended)

#### Literature

Opinion Exchange Dynamics Elchanan Mossel und Omer Tamuz Interacting particle systems for opinion dynamics: the Deffuant model and some generalizations Timo Hirscher

#### Informations

We hope to have the seminar in presence, probably in blocked form towards the end of the term. The precise dates will be fixed together with the participants.

#### Language

#### Number of places

#### Content

Random graphs are used as probabilistic models for complex networks. In the seminar we want to study several well know random graph models including the Erdös-Renyi random graph and the preferential attachment model. In particular, we will study the phase transition for the Erdös-Renyi random graph. During the seminar, we will learn important tools in the study of stochastic processes including couplings, stochastic order, probabilistic bounds and branching processes.

#### Requirements

Einführung in die Wahrscheinlichkeitstheorie und Statistik (MA0009) oder Einführung in die Wahrscheinlichkeitstheorie MA1401

#### Literature

R. van der Hofstad. Random Graphs and Complex Networks. Volume 1. Cambridge Series in Statistical and Probabilistic Mathematics (2017)

#### Informations

https://www-m5.ma.tum.de/Allgemeines/MA6011_2021W Es wird eine Vorbesprechung über Zoom stattfinden, bei der die Vortragsthemen verteilt werden.

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tba

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tba

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http://www.hairer.org/notes/RoughPaths.pdf https://arxiv.org/pdf/1603.03788.pdf https://arxiv.org/abs/1810.10971 https://arxiv.org/abs/2005.08897 https://arxiv.org/pdf/1905.08494.pdf more literature will be added at a later time

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Topologische Räume Stetigkeit Zusammenhang Kompaktheit Dimension Metrisierbarkeitssätze Polnische Räume Themen der deskriptiven Mengenlehre (Borel-Mengen, projektive Mengen, Determiniertheit) Topological Spaces Continuity Connected Spaces Compact Spaces Dimension Metrization Theorems Polish Spaces Selected Topics in Descriptive Set Theory (Borel sets, projective sets, Determinacy)

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Mathematische Grundvorlesungen

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Sieradski: Topology and Homotopy Dugundji: Topology Kechris: Classical Descriptive Set Theory

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Das Seminar ist ein gemeinsamer Lektüre- und Diskussionskurs des Buches "Algorithms from the Book" von Kenneth Lange (SIAM, 2020). Es beschäftigt sich mit berühmten und erfolgreichen Algorithmen und ihren mathematischen Grundlagen. Kenneth Lange arbeitet derzeit an einer Neuauflage des Buches. Wir werden neue Kapitel zur preview benutzen dürfen.

#### Requirements

Solide Kenntnisse in Analysis, linearer Algebra und Numerik.

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

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Chains of infinite order, first introduced by Doblin and Fortet in 1937, are the generalization of k-step Markov chains when the parameter k approaches infinity. The study of those chains is of significance in a variety of fields, such as Probability Theory, Statistical Mechanics and Ergodic Theory. For further information, please visit the seminar's website https://www-m5.ma.tum.de/Allgemeines/CIO_2021W

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Introduction to Probability and Statistics, Markov Chains, Measure Theory

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We will read several old and new papers together. Please visit the website of the seminar https://www-m5.ma.tum.de/Allgemeines/CIO_2021W for a list of those papers.

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Functional inequalities provide a method to compare functions to each other in view of certain features. How symmetric is a function under certain operations? How wiggly is it? How close is it to a given set functions? Such questions play an important role in mathematical physics, differential geometry, PDE analysis and many more fields, and functional inequalities give an answer in terms of robust integral expression. In this seminar, we shall encounter several well-known functional inequalities, like rearrangement, Hardy-Littlewood-Sobolev, logarithmic Sobolev and Hausdorff-Young inequalities. The proofs will provide information on the optimal constants and the optimizers, which achieve equality. In each case, the method of proof rests on some deep insight and has an inherent beauty. Applications, for instance to the estimate on the rates of equilibration in particle systems or to bound the Ricci curvature of manifolds, will be discussed depending on the interest of the participants.

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Analysis, LADS and Maßtheorie are a must. Basic knowledge in functional analysis and/or PDEs is helpful for some topics, but is not at all necessary to enjoy the seminar.

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For the specific functional inequalities mentioned above, we follow E.Lieb und M.Loss: "Analysis" (GSM 14, AMS). For further inequalities and the mentioned applications, additional material will be provided.

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This seminar is based on the book “An introduction to infinite-dimensional analysis” by Guiseppe da Prato (Springer, 2006). We will discuss stochastic concepts such as Gaussian measures in Hilbert spaces, Brownian motion and gradient systems. The topic brings together concepts from analysis, probability and statistical mechanics, such as Markov semigroups, stochastic dynamical systems and invariant measures. The book is pedagogical, but a background in functional analysis, measure theory and probability is advantageous. Concepts such as integration in Banach spaces will be introduced as required.

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The book is pedagogical, but a background in functional analysis, measure theory and probability is advantageous.

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Guiseppe da Prato, An introduction to infinite-dimensional analysis, Springer 2006

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Linear algebraic groups are an important class of groups that come with the structure of an algebraic variety. Examples include the general linear group, the special linear group or the orthogonal group over a field. In this seminar, we will develop the foundations of the theory of linear algebraic groups. We will discuss the basic definitions, important subgroups such as tori and Borel subgroups, the relationship between a linear algebraic group and its Lie algebra, as well as the root datum of a linear algebraic group. The endpoint of the seminar will be a discussion of the classification of reductive groups. The most important tools for our course come from linear algebra and algebraic geometry. The necessary prerequisites from algebraic geometry will be explained in the seminar, with the level of detail depending on the participants' backgrounds. The theory of linear algebraic groups has a number of applications in algebraic geometry, finite group theory and many other subjects. Moreover, while the foundations are well-understood and accessible, open questions related to linear algebraic groups are ubiquitous in modern mathematical research.

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Commutative Algebra within the scope of Algebra 2 Experience with algebraic geometry is very helpful, but not required

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T.A. Springer . Linear Algebraic Groups J.E. Humphreys. Linear Algebraic Groups R. Carter, G. Segal, I. Macdonald. Lectures on Lie Groups and Lie Algebras

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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.

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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)

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The material discussed in the seminar is based on recent research papers. Examples are: Physics-informed Deep Learning for Scientific Computing https://arxiv.org/abs/2103.09655 Three Ways to Solve Partial Differential Equations with Neural Networks -- A Review https://arxiv.org/abs/2102.11802 The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems https://link.springer.com/article/10.1007/s40304-018-0127-z Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control https://arxiv.org/abs/2105.14094 Efficient training of physics‐informed neural networks via importance sampling https://onlinelibrary.wiley.com/doi/abs/10.1111/mice.12685 A deep surrogate approach to efficient Bayesian inversion in PDE and integral equation models. https://arxiv.org/abs/1910.01547 Adaptive Physics-Informed Neural Networks for Markov-Chain Monte Carlo https://arxiv.org/abs/2008.01604 Data-driven discovery of coordinates and governing equations https://arxiv.org/abs/1904.02107 Towards physics-informed deep learning for turbulent flow prediction https://arxiv.org/abs/1911.08655 VAMPnets for deep learning of molecular kinetics https://arxiv.org/abs/1710.06012 SchNet: A continuous-filter convolutional neural network for modeling quantum interactions https://arxiv.org/abs/1706.08566 Clebsch–Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network https://arxiv.org/abs/1806.09231

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Die 5 Export-Plätze sind für Studierende der Fakultät Maschinenwesen/Mechanical Engineering