Seminars and workshops

Dates for seminars in the winter semester 2019/20

Kalender blau: Grafik: Kathrin Ruf

9 July 2019: Program announced for winter semester 2019/20

15 July (12 o'clock) - 21 July 2019: Students register using TUMonline

22 July - 26 July 2019: First round

29 July (12 o'clock) - 4 August 2019: Students register (second choice) using TUMonline

5 August - 9 August 2019: Second round

How are seminar places allocated?

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

You register using TUMonline 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. Should you not get a place, then you will be informed via e-mail.

Should you not receive a place in the seminar or workshop you indicated in stage 1, you can apply again using TUMonline for one of the available places in another seminar. The supervising tutors make a selection from the list of applicants.

The Examination Board allocates free places to students who were not allocated a place in stages 1 or 2. If you have not yet been allocated a place, please submit an informal application indicating your preferences (non-binding) from those seminar or workshop places remaining to:

Advanced seminars for Bachelor students

Please note:

For each advanced seminar offered to Bachelor's and Master’s students, there is a separate registration process in TUMonline. Please only register for advanced seminars labeled “Bachelor”. Places in the advanced seminars labeled “Master” are reserved for Master’s students who are already enrolled in these degree programs.
After the second selection round, current Bachelor's students and external Master’s applicants 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 seminars offered in the winter semester 2019/2020

The seminars of the Hurwitz-Gesellschaft can also be recognized as Bachelor seminars.

Sprache

deutsch

Anzahl an Plätzen

Bachelor Studierende: 6
Studierende anderer Fakultäten: None

Inhalt

In dem Seminar sollen verschiedene diskrete stochastische Modelle besprochen werden. Insbesondere werden wir Irrfahrten auf Graphen, Markovsche Felder und Zufallsgraphen betrachten.

Voraussetzungen

Probability theory (MA2409)

Literatur

Pierre Bremaud: Discrete Probability Models and Methods. Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding. Springer, 2017.

Informationen

https://www-m5.ma.tum.de/Allgemeines/MA6011_2019W Die Vortragssprache wird mit den Studierenden abgesprochen.

Sprache

deutsch

Anzahl an Plätzen

Bachelor Studierende: 8
Studierende anderer Fakultäten: 2

Inhalt

Fraktale Strukturen spielen eine wichtige Rolle in der Natur underöffnen spannende mathematische Fragestellungen. So weisenVerästelungen von Pflanzen, die Geographie von Küsten-Linien, oder dasWachstum von Kristallen selbstähnliche Strukturen auf. Schlüssel fürdie Erzeugung solcher Strukturen sind oftmals rekursive Algorithmenoder spezielle dynamischen Systeme. Bekannten Bilder wie dieMandelbrot-Menge, das Sierpinksi-Dreieck, die Drachenkurve oder derLorenz-Attraktor können so erzeugt werden. Die Spannweite der Themendeckt sowohl theoretische Fragestellungen wie auch algorithmischorientierte Aufgaben mit Anwendungsbezug ab. Spezialliteratur wirdwährend der Vorbesprechung bekanntgegeben.

Voraussetzungen

Analysis 1&2, Lineare Algebra und Diskrete Strukturen 1&2, Programmier Kenntnisse (z.B. MATLAB) , Einführung in die Numerische lineare Algebra

Literatur

* K. Bräuer - Chaos, Attraktoren und Fraktale. Mathematische und physikalische Grundlagen nichtlinearer Phänomene mit Anwendungen in Physik, Biologie und Medizin * Kenneth Falconer - Fractal geometry * Peitgen Heinz-Otto - Chaos and fractals

Informationen

Die erste Vorbesprechung wird voraussichtlich am 13.08. (oder nach individueller Vereinbarung) stattfinden.

Sprache

englisch

Anzahl an Plätzen

Bachelor Studierende: 6
Studierende anderer Fakultäten: None

Inhalt

The seminar focuses on algorithmic geometry at an introductory level. Topics include algorithms for computing, e.g., triangulations, Voronoi cells, and convex hulls. In addition to the theoretical foundations we will also discuss applications from fields such as computer graphics and robotics.

Voraussetzungen

Necessary: * Algorithmic Discrete Mathematics (MA2501) Recommended: * Fundamentals of Convex Optimization (MA2504)

Literatur

de Berg M., van Kreveld M., Overmars M., Schwarzkopf O.C. (2000) Computational Geometry. Springer Joswig M., Theobald T. (2013) Polyhedral and Algebraic Methods in Computational Geometry. Springer

Informationen

The presentations will take place in English. More information will be provided before the start of the semester.

Sprache

englisch

Anzahl an Plätzen

Bachelor Studierende: 6
Studierende anderer Fakultäten: None

Inhalt

Cancer is a wide-spread disease group in human population, and many scientists from different disciplines are working on a better understanding the underlying processes and finding efficient therapies. In this seminar, we want to learn about mathematical aspects of tumour growth and how mathematical models can be used to describe tumour evolution. This helps to understand better the mechanisms behind and how treatments act and can be used in an optimal way. Often, the dynamic behaviour is described by differential equation models. PDEs allow e.g. for considering spatial models, like for a spatially heterogeneous solid tumour, and by a kind of age structure, for the formation of metastases, describing malignant tumours. Analysis helps to understand the qualitative behaviour of these models, especially for long terms. But also concrete studies and numerical simulations might be useful to consider.

Voraussetzungen

Previous knowledge recommended: Differential equations, Math. Models in Biology

Literatur

This seminar will be based mainly on recent papers on the topic.

Informationen

The selection of topics will be done in accordance with the participants, taking into account the individual previous knowledge.

Sprache

englisch

Anzahl an Plätzen

Bachelor Studierende: 4
Studierende anderer Fakultäten: 5

Inhalt

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.

Voraussetzungen

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).

Literatur

The seminar will mostly be based on the books "Economics and Computation" by David C. Parkes and Sven Seuken (http://economicsandcomputation.org/), which will be available for download for participants of the seminar, and the "Handbook of Computational Social Choice" by Felix Brandt, Vincent Conitzer, Ulle Endriss, Jérôme Lang, and Ariel D. Procaccia (http://www.cambridge.org/download_file/951600).

Informationen

There is seminar overview (Vorbesprechung) on Wednesday, July 17, 2019 at 16.00 in room 01.10.011. The seminar takes place in a blocked form, i.e., there will be two full-day meetings; dates tbd. Participation is required for passing the seminar. All students have to apply for the seminar. Further information (including the application procedure) can be found on the course homepage: http://dss.in.tum.de/teaching

Sprache

deutsch

Anzahl an Plätzen

Bachelor Studierende: 8
Studierende anderer Fakultäten: None

Inhalt

Im Seminar werden Neuronale Netze aus mathematischer Perspektive analysiert. Die behandelten Themen beinhalten u.a. Resultate aus der Approximationstheorie, der statistischen Lerntheorie und der Optimierungstheorie.

Voraussetzungen

Analysis 1,2 LADS 1,2 Grundlagen der Statistik und W-Theorie

Literatur

tba

Informationen

Sprache

deutsch

Anzahl an Plätzen

Bachelor Studierende: 10
Studierende anderer Fakultäten: None

Inhalt

Das Aufkommen von 3D Druckverfahren eröffnet der mathematischen Visualisierung neue Möglichkeiten. Veranschaulichungen mathematischen Sachverhalte und Objekte können relativ einfach 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 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.

Voraussetzungen

Analysis und Lineare Algebra. Differentialgeometrie: Grundlagen und/oder Geometriekalküle, Programmiererfahrung

Literatur

Je nach zu bearbeitendem Modell passende Fachartikel

Informationen

Sprache

englisch

Anzahl an Plätzen

Bachelor Studierende: 4
Studierende anderer Fakultäten: 2

Inhalt

The goal of this seminar is to approach the main concepts of category theory from various directions, motivated by concrete examples and applications. After an introduction to the basic notions, we will discuss various contexts in which categories can play a clarifying role, highlighting the purpose of unifying and connecting mathematical concepts. We will cover classical examples from algebra and topology, but also several unexpected applications.

Voraussetzungen

Most of the examples will be drawn from Algebra, Topology, and Differential Geometry. Familiarity with at least some of these areas will be very helpful but not required.

Literatur

Martin Brandenburg: Einführung in die Kategorientheorie (https://link-springer-com.eaccess.ub.tum.de/book/10.1007%2F978-3-662-47068-8) Tom Leinster: Basic Category Theory (http://www.maths.ed.ac.uk/~tl/bct/) Emily Riehl: Category theory in context (http://www.math.jhu.edu/~eriehl/context.pdf)

Informationen

Sprache

deutsch

Anzahl an Plätzen

Bachelor Studierende: 13
Studierende anderer Fakultäten: 3

Inhalt

Im Mittelpunkt des Seminars soll die qualitative und geometrische Theorie nichtlinearer gewöhnlicher Differentialgleichungen stehen. Hierzu werden wir uns zunächst mit der Analysis auf Mannigfaltigkeiten beschäftigen. Im Anschluß sollen dann mit Hilfe dieser Methoden verschiedene grundlegende Resultate aus der Theorie dynamischer Systeme bewiesen werden. Einige Höhepunkte werden dabei das Theorem von Hartman-Grobman (nebst Satz über die stabile Mannigfaltigkeit), das Kupka-Smale Theorem sowie Peixoto's Theorem sein. Bei Interesse sind auch weiterführende Themen möglich.

Voraussetzungen

Analysis, Gewöhnliche Differentialgleichungen, nach Möglichkeit: Nonlinear Dynamics.

Literatur

Jacob Palis und Welington de Melo: Geometric Theory of Dynamical Systems. An Introduction, Springer-Verlag Berlin, 1982.

Informationen

Voraussichtlicher Termin: Do 14-16 Uhr. Die maximale Teilnehmerzahl beträgt 13.

Sprache

englisch

Anzahl an Plätzen

Bachelor Studierende: 4
Studierende anderer Fakultäten: None

Inhalt

In this seminar we will discuss selected topics in optimal transport. Particular focus will be on multi-marginal problems for costs such as the Coulomb or Wasserstein barycenter cost and static and dynamic methods for interpolating between different probability measures. The seminar will cover analytical issues, modelling, and algorithms, depending on the taste of the participants. The seminar mainly builds upon the material covered in MA 5934 (Optimal transport) in the summer term 2019.

Voraussetzungen

MA5934

Literatur

C. Villani, Topics in Optimal Transportation, AMS 2003 F.Santambrogio, Optimal Transport for Applied Mathematicians, Birkhaeuser 2015 G.Peyre, M.Cuturi, Computational Optimal Transport, https://arxiv.org/abs/1803.00567

Informationen

Sprache

englisch

Anzahl an Plätzen

Bachelor Studierende: 4
Studierende anderer Fakultäten: 2

Inhalt

Funktionalungleichungen dienen zum Vergleich von Integralausdrücken, in denen eine oder mehrere Funktionen als "Variablen" auftreten. Ein elementares, aber extrem wichtiges Beispiel ist die Cauchy-Schwarz-Ungleichung, die Ihnen vermutlich am Ende von Analysis 2 bewiesen wurde: hier wird das Integral über das Produkt fg zweier beliebiger Funktionen f und g nach oben abgeschätzt mithilfe der Integrale über die Quadrate f^2 und g^2. Im Seminar werden wir kompliziertere Beispiele diskutieren und beweisen, unter anderem die Youngsche, die logarithmische Sobolev- und die Hardy-Littlewood-Sobolev-Ungleichungen. Die teilweise geradezu genialen Beweise benutzen u.a. elementare aber tiefsinnige geometrische Konstruktionen, nicht offensichtliche Symmetrien oder überraschende Dualitätsbeziehungen. Außerdem werden wir auf die fundamentale Bedeutung von Funktionalungleichungen in der Theorie der partiellen Differentialgleichungen, der Differentialgeometrie, der mathematischen Physik usw. eingehen. So werden wir sehen, wie sich die Konstanten in bestimmten Ungleichungen interpretieren lassen als Geschwindigkeit, mit der ein physikalisches Teilchensystem ins thermische Gleichgewicht geht, als Schranke an die Krümmung einer Mannigfaltigkeit usw.

Voraussetzungen

Teilnehmer/innen sollten Analysis 1+2 sowie Vektoranalysis und Maß-/Integrationstheorie erfolgreich abgeschlossen haben. Grundkenntnisse in Funktionalanalysis und/oder partiellen Differentialgleichungen erleichtern das Verstehen gelegentlich, sind aber nicht notwendig.

Literatur

Zu Beginn folgen wir dem Buch von E.Lieb und M.Loss: "Analysis" (GSM 14, AMS). In den späteren Vorträgen sollen Teile aus ausgewählten Forschungsartikeln vorgestellt werden.

Informationen

Fragen zum Seminar können Sie mir gern per Email stellen.

Sprache

englisch

Anzahl an Plätzen

Bachelor Studierende: 4
Studierende anderer Fakultäten: None

Inhalt

We study the rate at which various markov chains converge to their limiting distributions. The methods involved come from variety of fields such as probability theory, analysis, combinatorics and algebra.

Voraussetzungen

Probability Theory, Markov chains

Literatur

Markov Chains and Mixing Times by D. A. Levin, Y. Peres and E. L. Wilmer. Available at https://pages.uoregon.edu/dlevin/MARKOV/markovmixing.pdf

Informationen

The seminar will take place in English, and will possibly be blocked.

Sprache

englisch

Anzahl an Plätzen

Bachelor Studierende: 3
Studierende anderer Fakultäten: None

Inhalt

Modern scientific studies (e.g., genome-wide association studies in biology) produce large-scale data whose analysis routinely involves tests of many different hypotheses. Controlling the number of false discoveries made by the many different statistical tests is then of crucial importance in order to arrive at sound scientific conclusions. In this seminar we study methods for control of the false discovery rate, starting with the celebrated work of Benjamini and Hochberg from the mid-1990s and moving to innovative new approaches such as the knock-off method of Barber and Candes.

Voraussetzungen

Probability Theory, Statistik: Grundlagen

Literatur

Selected research articles and book chapters, e.g., Benjamini, Yoav; Hochberg, Yosef Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. Roy. Statist. Soc. Ser. B 57 (1995), no. 1, 289–300. Barber, Rina Foygel; Candès, Emmanuel J. Controlling the false discovery rate via knockoffs. Ann. Statist. 43 (2015), no. 5, 2055–2085.

Informationen

The seminar will be offered in blocks on 3-4 Fridays.

Sprache

deutsch

Anzahl an Plätzen

Bachelor Studierende: 6
Studierende anderer Fakultäten: None

Inhalt

Teilbarkeit, Primzahlen, Kongruenzen, Eulersche Phi-Funktion, Quadratisches Reziprozitätsgesetz, Arithmetische Funktionen, Primzahlsatz, Bertrandsches Postulat, Arithmetische Progressionen

Voraussetzungen

Mathematische Grundvorlesungen (Lineare Algebra, Analysis)

Literatur

Nathanson: Elementary Methods in Number Theory. Springer Hardy/Wright: An Introduction to the Theory of Numbers, Oxford University Press

Informationen

Sprache

englisch

Anzahl an Plätzen

Bachelor Studierende: 6
Studierende anderer Fakultäten: None

Inhalt

Eugene Wigner was surprised by the observation that the absorption spectrum of heavy atoms are very similar. The special structure of the atoms only has a minor influence. Step by step it became clear, that this observation can be understood based on the theory of random matrices. Random matrices are matrices, where the entries are random variables (e.g., normally distributed). If the dimension of the matrix is large, the eigenvalues mainly depend on the structure of the matrix (symmetry, band structure etc.), but not on the given realization of the random variables. The resulting distributions of eigenvalues seem to describe distributions with a universal character, similarly to the omnipresent normal distribution. In the seminar, we will consider the basic theory of random matrices, as well as applications of the distributions. Note: Please consider to take part in our information event, or contact Volker Hoesel (Hoesel@t-online.de) or Johannes Mueller (johannes.mueller@mytum.de) directly. We would like to talk to the interested students to know the interests and the level of applicants, and to adapt the seminar topics accordingly. We will only accept students who did contact us beforehand. Information event: Friday, 12'th Juli, 14:15 In the seminar room 02.08.020.

Voraussetzungen

Grundvorlesungen Analysis, Grundlagen Stochastik erwünscht.

Literatur

Non-mathematical article: Bertrand Eynard, Neue universelle Gesetze , Spektrum der Wissenschaft, Oktober 2018 Textbook: Anderson, Guinnet, Zeitouni, An introduction to random matrices, Cambridge Univ. Press, 2009 Various articles for applications.

Informationen

Advanced seminars for Masters students

Places in the advanced seminars labeled “Master” are generally allocated to Master’s students who are already enrolled in these degree programs! They may register for one advanced seminar only.
After the second 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 in 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 2019/2020

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 20
Studierende anderer Fakultäten: None

Inhalt

Current topics in Deep Learning.

Voraussetzungen

Basic understanding of linear algebra, calculus, and probability theory.

Literatur

Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning. MIT press. Scientific Papers

Informationen

Block seminar at the Institute of Computational Biology, Helmholtz Center Munich.

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 8
Studierende anderer Fakultäten: 4

Inhalt

Recent research at the interplay of machine learning and discrete optimization. Discrete optimization problems are becoming increasingly important in machine learning. We will identify some of these problems as well as structures that make it possible to efficiently obtain exact or approximate solutions even at very large scales. On the other hand, well-established solution methods for NP-hard discrete optimization problems may benefit from the application of learning techniques. We will study how machine learning can improve the design of exact and heuristic algorithms in discrete optimization. Students are expected to read and thoroughly understand original research papers, and to deliver an oral presentation.

Voraussetzungen

Discrete Optimization (MA3502) or Combinatorial Optimization (MA 4502); Machine Learning (IN2064) or Statistical Modeling and Machine Learning (IN2332).

Literatur

A list of original research papers will be handed out shortly before the start of the term. Students are required to pick a paper during first week of classes.

Informationen

Students will give oral presentations on their papers in December.

Sprache

deutsch

Anzahl an Plätzen

Master Studierende: 6
Studierende anderer Fakultäten: None

Inhalt

In dem Seminar sollen verschiedene diskrete stochastische Modelle besprochen werden. Insbesondere werden wir Irrfahrten auf Graphen, Markovsche Felder und Zufallsgraphen betrachten.

Voraussetzungen

Probability theory (MA2409)

Literatur

Pierre Bremaud: Discrete Probability Models and Methods. Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding. Springer, 2017.

Informationen

https://www-m5.ma.tum.de/Allgemeines/MA6011_2019W Die Vortragssprache wird mit den Studierenden abgesprochen.

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 2
Studierende anderer Fakultäten: 2

Inhalt

Funktionalungleichungen dienen zum Vergleich von Integralausdrücken, in denen eine oder mehrere Funktionen als "Variablen" auftreten. Ein elementares, aber extrem wichtiges Beispiel ist die Cauchy-Schwarz-Ungleichung, die Ihnen vermutlich am Ende von Analysis 2 bewiesen wurde: hier wird das Integral über das Produkt fg zweier beliebiger Funktionen f und g nach oben abgeschätzt mithilfe der Integrale über die Quadrate f^2 und g^2. Im Seminar werden wir kompliziertere Beispiele diskutieren und beweisen, unter anderem die Youngsche, die logarithmische Sobolev- und die Hardy-Littlewood-Sobolev-Ungleichungen. Die teilweise geradezu genialen Beweise benutzen u.a. elementare aber tiefsinnige geometrische Konstruktionen, nicht offensichtliche Symmetrien oder überraschende Dualitätsbeziehungen. Außerdem werden wir auf die fundamentale Bedeutung von Funktionalungleichungen in der Theorie der partiellen Differentialgleichungen, der Differentialgeometrie, der mathematischen Physik usw. eingehen. So werden wir sehen, wie sich die Konstanten in bestimmten Ungleichungen interpretieren lassen als Geschwindigkeit, mit der ein physikalisches Teilchensystem ins thermische Gleichgewicht geht, als Schranke an die Krümmung einer Mannigfaltigkeit usw.

Voraussetzungen

Teilnehmer/innen sollten Analysis 1+2 sowie Vektoranalysis und Maß-/Integrationstheorie erfolgreich abgeschlossen haben. Grundkenntnisse in Funktionalanalysis und/oder partiellen Differentialgleichungen erleichtern das Verstehen gelegentlich, sind aber nicht notwendig.

Literatur

Zu Beginn folgen wir dem Buch von E.Lieb und M.Loss: "Analysis" (GSM 14, AMS). In den späteren Vorträgen sollen Teile aus ausgewählten Forschungsartikeln vorgestellt werden.

Informationen

Fragen zum Seminar können Sie mir gern per Email stellen.

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 6
Studierende anderer Fakultäten: None

Inhalt

Cancer is a wide-spread disease group in human population, and many scientists from different disciplines are working on a better understanding the underlying processes and finding efficient therapies. In this seminar, we want to learn about mathematical aspects of tumour growth and how mathematical models can be used to describe tumour evolution. This helps to understand better the mechanisms behind and how treatments act and can be used in an optimal way. Often, the dynamic behaviour is described by differential equation models. PDEs allow e.g. for considering spatial models, like for a spatially heterogeneous solid tumour, and by a kind of age structure, for the formation of metastases, describing malignant tumours. Analysis helps to understand the qualitative behaviour of these models, especially for long terms. But also concrete studies and numerical simulations might be useful to consider.

Voraussetzungen

Previous knowledge recommended: Differential equations, Math. Models in Biology

Literatur

This seminar will be based mainly on recent papers on the topic.

Informationen

The selection of topics will be done in accordance with the participants, taking into account the individual previous knowledge.

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 1
Studierende anderer Fakultäten: 5

Inhalt

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.

Voraussetzungen

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).

Literatur

The seminar will mostly be based on the books "Economics and Computation" by David C. Parkes and Sven Seuken (http://economicsandcomputation.org/), which will be available for download for participants of the seminar, and the "Handbook of Computational Social Choice" by Felix Brandt, Vincent Conitzer, Ulle Endriss, Jérôme Lang, and Ariel D. Procaccia (http://www.cambridge.org/download_file/951600).

Informationen

There is seminar overview (Vorbesprechung) on Wednesday, July 17, 2019 at 16.00 in room 01.10.011. The seminar takes place in a blocked form, i.e., there will be two full-day meetings; dates tbd. Participation is required for passing the seminar. All students have to apply for the seminar. Further information (including the application procedure) can be found on the course homepage: http://dss.in.tum.de/teaching

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 6
Studierende anderer Fakultäten: None

Inhalt

This semester's edition of the seminar will focus on Compressive Sensing. The theory of Compressive Sensing formalizes the idea that a smart, often random, parameter choice in a measurement system can make an inverse problem less ill posed. The mathematical analysis of this problem combines techniques from high dimensional probability theory, convex and non-convex optimization, linear algebra, and many other areas in mathematics.

Voraussetzungen

Probability Theory, Foundations of Data Analysis and/or Probabilistic Methods and Algorithms in Data Analysis would be useful

Literatur

S. Foucart, H. Rauhut: A Mathematical Introduction to Compressive Sensing, Springer 2013 Further literature will be recommended when the topics are assigned.

Informationen

The seminar will be offered in blocks on 1-2 afternoons.

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 12
Studierende anderer Fakultäten: None

Inhalt

In this seminar students will learn techniques for sports data analytics. Students will choose a sport of their choice that has a next generation big data set from one or more of the many open domain repositories, with Kaggle a preference. Students will also perform research on statistical methodologies for their sport by selection of one or more articles from a sports analytics journal, with the Journal of Quantitative Analysis in Sports a preference. They will use Tableau to interactively visualize their data, which can be downloaded from its website. And finally, they will produce leading edge data science seminars. Because of high demand, please note the following rules for the seminar and do not register if they cannot be followed. All deadlines have to be met in order to pass the course, including confirmation of acceptance during the registration period, requests for more detailed project proposals before the lecture period starts, and the submission of seminars before presentation. Details are provided by email so students must be reachable by email. Failure to meet a deadline results in automatic de-registration from the course. Attendance at all seminars, Thursdays 2 – 4 throughout the lecture period except for Dec 19 2019, is mandatory and failure to attend results in automatic failure. Upon demonstration of sufficient motivation and progress in the seminar, students may be offered the opportunity to write their Master’s thesis under the supervision of Prof. Ankerst. The topic must be the same as that presented for the seminar and the student must register to start no later than April 1 2020. Students interested in registering for the course should provide current TUM Master grade transcripts an application letter less than one page identifying a top preference for the sport to be studied, relevant data sets along with confirmation that they have been downloaded, and research articles of interest related to the sport. to Prof. Donna Ankerst (ankerst@tum.de) by 5pm on July 30, 2019.

Voraussetzungen

Data Science, R, and Applied Regression courses

Literatur

Internet sources Kaggle, Tableau, Journal of Quantitative Analysis in Sports

Informationen

Thursdays 14 - 16

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 8
Studierende anderer Fakultäten: None

Inhalt

We discuss univariate and multivariate extreme-value theory on both a theoretical and applied level. Univariate theory encompasses classical limit results for order statistics, the peaks-over-threshold method and estimation. Multivariate theory focuses on the dependence among extreme events. Applications are considered from the insurance industry, mostly from non-life and operational risk. Each participant presents one of the selected papers and discusses subsequent developments in the respective field. This provides a broad overview to all participants on the different topics, re-cent aspects, and historical development of the topics.

Voraussetzungen

“Stochastic Analysis”, “Continuous Time Finance”

Literatur

visit our webpage at https://www.mathfinance.ma.tum.de/en/teaching/wintersemester-201920/

Informationen

Preliminary Meeting on July 18th at 14:00 in Seminarroom 2.01.11 in Garching Hochbrück

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 5
Studierende anderer Fakultäten: None

Inhalt

Modern scientific studies (e.g., genome-wide association studies in biology) produce large-scale data whose analysis routinely involves tests of many different hypotheses. Controlling the number of false discoveries made by the many different statistical tests is then of crucial importance in order to arrive at sound scientific conclusions. In this seminar we study methods for control of the false discovery rate, starting with the celebrated work of Benjamini and Hochberg from the mid-1990s and moving to innovative new approaches such as the knock-off method of Barber and Candes.

Voraussetzungen

Probability Theory, Statistik: Grundlagen

Literatur

Selected research articles and book chapters, e.g., Benjamini, Yoav; Hochberg, Yosef Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. Roy. Statist. Soc. Ser. B 57 (1995), no. 1, 289–300. Barber, Rina Foygel; Candès, Emmanuel J. Controlling the false discovery rate via knockoffs. Ann. Statist. 43 (2015), no. 5, 2055–2085.

Informationen

The seminar will be offered in blocks on 3-4 Fridays.

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 6
Studierende anderer Fakultäten: 2

Inhalt

The goal of this seminar is to approach the main concepts of category theory from various directions, motivated by concrete examples and applications. After an introduction to the basic notions, we will discuss various contexts in which categories can play a clarifying role, highlighting the purpose of unifying and connecting mathematical concepts. We will cover classical examples from algebra and topology, but also several unexpected applications.

Voraussetzungen

Most of the examples will be drawn from Algebra, Topology, and Differential Geometry. Familiarity with at least some of these areas will be very helpful but not required.

Literatur

Martin Brandenburg: Einführung in die Kategorientheorie (https://link-springer-com.eaccess.ub.tum.de/book/10.1007%2F978-3-662-47068-8) Tom Leinster: Basic Category Theory (http://www.maths.ed.ac.uk/~tl/bct/) Emily Riehl: Category theory in context (http://www.math.jhu.edu/~eriehl/context.pdf)

Informationen

Sprache

deutsch

Anzahl an Plätzen

Master Studierende: 13
Studierende anderer Fakultäten: 3

Inhalt

Im Mittelpunkt des Seminars soll die qualitative und geometrische Theorie nichtlinearer gewöhnlicher Differentialgleichungen stehen. Hierzu werden wir uns zunächst mit der Analysis auf Mannigfaltigkeiten beschäftigen. Im Anschluß sollen dann mit Hilfe dieser Methoden verschiedene grundlegende Resultate aus der Theorie dynamischer Systeme bewiesen werden. Einige Höhepunkte werden dabei das Theorem von Hartman-Grobman (nebst Satz über die stabile Mannigfaltigkeit), das Kupka-Smale Theorem sowie Peixoto's Theorem sein. Bei Interesse sind auch weiterführende Themen möglich.

Voraussetzungen

Analysis, Gewöhnliche Differentialgleichungen, nach Möglichkeit: Nonlinear Dynamics.

Literatur

Jacob Palis und Welington de Melo: Geometric Theory of Dynamical Systems. An Introduction, Springer-Verlag Berlin, 1982.

Informationen

Voraussichtlicher Termin: Do 14-16 Uhr. Die maximale Teilnehmerzahl beträgt 13.

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 6
Studierende anderer Fakultäten: 2

Inhalt

We will focus on open problems in quantum information theory. These are connected to various modern topics, ranging from information measures, quantum communication and computation, to many-body quantum physics.

Voraussetzungen

Prerequisite: Mathematical Introduction to Quantum Information Processing [MA5057] (or equivalent) A solid understanding of basic concepts of quantum information theory will be assumed.

Literatur

TBA. Primary sources will be research papers (rather than textbook materials).

Informationen

For additional information, see http://www-m5.ma.tum.de/Allgemeines/Lehrveranstaltungen

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 6
Studierende anderer Fakultäten: None

Inhalt

In this seminar we will discuss selected topics in optimal transport. Particular focus will be on multi-marginal problems for costs such as the Coulomb or Wasserstein barycenter cost and static and dynamic methods for interpolating between different probability measures. The seminar will cover analytical issues, modelling, and algorithms, depending on the taste of the participants. The seminar mainly builds upon the material covered in MA 5934 (Optimal transport) in the summer term 2019.

Voraussetzungen

MA5934

Literatur

C. Villani, Topics in Optimal Transportation, AMS 2003 F.Santambrogio, Optimal Transport for Applied Mathematicians, Birkhaeuser 2015 G.Peyre, M.Cuturi, Computational Optimal Transport, https://arxiv.org/abs/1803.00567

Informationen

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 4
Studierende anderer Fakultäten: None

Inhalt

The seminar focuses on algorithmic geometry at an introductory level. Topics include algorithms for computing, e.g., triangulations, Voronoi cells, and convex hulls. In addition to the theoretical foundations we will also discuss applications from fields such as computer graphics and robotics.

Voraussetzungen

Necessary: * Algorithmic Discrete Mathematics (MA2501) Recommended: * Fundamentals of Convex Optimization (MA2504)

Literatur

de Berg M., van Kreveld M., Overmars M., Schwarzkopf O.C. (2000) Computational Geometry. Springer Joswig M., Theobald T. (2013) Polyhedral and Algebraic Methods in Computational Geometry. Springer

Informationen

The presentations will take place in English. More information will be provided before the start of the semester.

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 6
Studierende anderer Fakultäten: None

Inhalt

We study the rate at which various markov chains converge to their limiting distributions. The methods involved come from variety of fields such as probability theory, analysis, combinatorics and algebra.

Voraussetzungen

Probability Theory, Markov chains

Literatur

Markov Chains and Mixing Times by D. A. Levin, Y. Peres and E. L. Wilmer. Available at https://pages.uoregon.edu/dlevin/MARKOV/markovmixing.pdf

Informationen

The seminar will take place in English, and will possibly be blocked.

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 20
Studierende anderer Fakultäten: None

Inhalt

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.

Voraussetzungen

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

Literatur

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.

Informationen

This is a literature seminar with weekly presentation of selected research papers from students at the Institute of Computational Biology, Helmholtz Zentrum München http://icb.helmholtz-muenchen.de/

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 8
Studierende anderer Fakultäten: None

Inhalt

For any p-adic Lie group G (such as GL_n(Q_p), SL_n(Q_p), Sp_2n(Q_p)) one can construct an associated Bruhat-Tits building. This is a complete metric space that can be constructed as a simplicial space, and which carries an action of the group G. It plays a central role in the classification of interesting subgroups of G, with applications both in arithmetic geometry and in representation theory for p-adic groups. In this seminar we will first construct the Bruhat-Tits building and study important examples before we consider applications of the theory.

Voraussetzungen

Algebra 2; basic knowledge of p-adic numbers; previous knowledge of linear algebraic groups or Lie groups is helpful but not mandatory

Literatur

Hauptreferenz: I. Macdonald, Spherical functions on a group of p-adic type, University of Madras, 1971, Chapter 2 Ergänzend (aber fortgeschrittener): J. Tits, Reductive groups over local fields, in: Proceedings of Symposia in pure mathematics 33 (1979), pp. 29-69

Informationen

Sprache

deutsch

Anzahl an Plätzen

Master Studierende: 6
Studierende anderer Fakultäten: None

Inhalt

Teilbarkeit, Primzahlen, Kongruenzen, Eulersche Phi-Funktion, Quadratisches Reziprozitätsgesetz, Arithmetische Funktionen, Primzahlsatz, Bertrandsches Postulat, Arithmetische Progressionen

Voraussetzungen

Mathematische Grundvorlesungen (Lineare Algebra, Analysis)

Literatur

Nathanson: Elementary Methods in Number Theory. Springer Hardy/Wright: An Introduction to the Theory of Numbers, Oxford University Press

Informationen

Sprache

englisch

Anzahl an Plätzen

Master Studierende: 6
Studierende anderer Fakultäten: None

Inhalt

Eugene Wigner was surprised by the observation that the absorption spectrum of heavy atoms are very similar. The special structure of the atoms only has a minor influence. Step by step it became clear, that this observation can be understood based on the theory of random matrices. Random matrices are matrices, where the entries are random variables (e.g., normally distributed). If the dimension of the matrix is large, the eigenvalues mainly depend on the structure of the matrix (symmetry, band structure etc.), but not on the given realization of the random variables. The resulting distributions of eigenvalues seem to describe distributions with a universal character, similarly to the omnipresent normal distribution. In the seminar, we will consider the basic theory of random matrices, as well as applications of the distributions. Note: Please consider to take part in our information event, or contact Volker Hoesel (Hoesel@t-online.de) or Johannes Mueller (johannes.mueller@mytum.de) directly. We would like to talk to the interested students to know the interests and the level of applicants, and to adapt the seminar topics accordingly. We will only accept students who did contact us beforehand. Information event: Friday, 12'th Juli, 14:15 In the seminar room 02.08.020.

Voraussetzungen

Grundvorlesungen Analysis, Grundlagen Stochastik erwünscht.

Literatur

Non-mathematical article: Bertrand Eynard, Neue universelle Gesetze , Spektrum der Wissenschaft, Oktober 2018 Textbook: Anderson, Guinnet, Zeitouni, An introduction to random matrices, Cambridge Univ. Press, 2009 Various articles for applications.

Informationen