Suchergebnis: Katalogdaten im Frühjahrssemester 2020

Mathematik Bachelor Information
Seminare
Dieses Semester haben viele Seminare eine Warteliste mit speziellem Auswahlverfahren. Falls keine anderen Auswahlkriterien vorliegen, werden bei der definitiven Belegung zuerst jene Studierenden berücksichtigt, welche noch keine andere Seminarbelegung haben. Wenn Sie sich in zwei Wartelisten eintragen, so tun Sie dies am besten so: wählen Sie zuerst das Seminar aus, das Sie bevorzugen, und wählen Sie anschliessend eine Ausweichmöglichkeit aus.
NummerTitelTypECTSUmfangDozierende
401-3180-20LIntroduction to Homotopy Theory and Model Category Structure Belegung eingeschränkt - Details anzeigen
Number of participants limited to 24.
W4 KP2SJ. Ducoulombier
KurzbeschreibungIntroductory seminar about category theory and techniques in Algebraic topology such as model category structure and "homotopy" limits and colimits.
LernzielIt is well known that topological spaces are endowed with a homotopy theory classifying objects up to continuous deformations. Model categories provide a natural setting for homotopy theory and it has been used in some parts of algebraic K-theory, algebraic geometry and algebraic topology, where homotopy-theoretic approaches led to deep results.


The goal of this seminar is to get an introduction to model structures through examples (topological spaces, simplicial sets, chains complexes...). To get further into this theory, we develop the notion of derived functors with applications to homotopy limits and colimits.
Literatur"Homotopy theories and model categories" Dwyer and Spalinski

"A primer on homotopy colimits" Dugger

"Model categories" Hovey
Voraussetzungen / BesonderesThe students are expected to be familiar with topological spaces
and fundamental groups.

This seminar takes the form of a working group, where interactions are encouraged. Participants are expected to attend the seminar, give a presentation and write a report. Topic will be assigned during the first meeting.
401-3200-69LA Survey of Geometric Group Theory Information Belegung eingeschränkt - Details anzeigen
Number of participants limited to 24.
W4 KP2SM. Cordes
KurzbeschreibungIn this class we will cover some of the tools, techniques, and groups central to the study of geometric group theory. After introducing the basic concepts (groups and metric spaces), we will branch out and sample different topics in geometric group theory based on the interest of the participants.
LernzielTo learn and understand a wide range of tools and groups central to the field of geometric group theory.
InhaltPossible topics include: properties of free groups and groups acting on trees, large scale geometric invariants (Dehn functions, hyperbolicity, ends of groups, asymptotic dimension, growth of groups), and examples of notable and interesting groups (Coxeter groups, right-angled Artin groups, lamplighter groups, Thompson's group, mapping class groups, and braid groups).
LiteraturThe topics will be chosen from "Office Hours with a Geometric Group Theorist" edited by Matt Clay and Dan Margalit.
Voraussetzungen / BesonderesOne should be familiar with the basics of groups, metric spaces, and topology (should be familiar with the fundamental group).
401-3030-19LDas Auswahlaxiom Belegung eingeschränkt - Details anzeigen
Maximale Teilnehmerzahl: 44.
Bei mehr als 30 Anmeldungen wird das Seminar doppelt geführt.
W4 KP2SL. Halbeisen
KurzbeschreibungEs werden verschiedene Aspekte des Auswahlaxioms untersucht. Einerseits werden Konsequenzen des Auswahlaxioms behandelt, andererseits werden auch Modelle der Mengenlehre konstruiert, in denen das Auswahlaxiom nicht gilt.
Lernziel
InhaltEs werden verschiedene Aspekte des Auswahlaxioms untersucht.

Im Seminar A, von 13-15 Uhr, werden äquivalente Formen und Konsequenzen des Auswahlaxioms behandelt

Im Seminar B, von 15-17 Uhr, werden Modelle der Mengenlehre konstruiert, in denen nur abgeschwächte Formen des Auswahlaxioms gelten, nicht aber das volle Auswahlaxiom.
401-3200-16LPower Sums of Coxeter Exponents (With Some Insight Into the Evolution of an Article) Belegung eingeschränkt - Details anzeigen
Number of participants limited to 12.
W4 KP2SR. Suter
KurzbeschreibungIn addition to its mathematical content, this seminar shall provide an insight into what is usually hidden away from the reader of an article.
LernzielThe gradual development from an initial wish to make progress on a certain topic towards a published article is usually hidden away in the final text. The idea of this seminar is to have a look at the two author paper "Power sums of Coxeter exponents" (Advances in Mathematics 231 (2012), 1291-1307), that arose entirely by means of email correspondence, and to make accessible some excerpts from this correspondence in order to gain some insight into how the article evolved. This might be instructive in particular with regard to the students' own research ambitions.
LiteraturJ. Burns, R. Suter: Power sums of Coxeter exponents, Adv. Math. 231 (2012), 1291-1307. www.sciencedirect.com/science/article/pii/S0001870812002411
Voraussetzungen / BesonderesNo prior knowledge of Coxeter exponents is required because some relevant stuff about Coxeter groups and root systems shall be explained in an early seminar talk.
401-3600-20LSeminar über Wahrscheinlichkeitstheorie Belegung eingeschränkt - Details anzeigen
Beschränkte Teilnehmerzahl.
Die Anmeldung erlangt erst Gültigkeit nach der Bestätigung per E-Mail durch die Veranstalter.
W4 KP2SA.‑S. Sznitman, J. Bertoin, V. Tassion, W. Werner
Kurzbeschreibung
Lernziel
401-3620-20LStudent Seminar in Statistics: Inference in Non-Classical Regression Models Belegung eingeschränkt - Details anzeigen
Maximale Teilnehmerzahl: 24
Hauptsächlich für Studierende der Bachelor- und Master-Studiengänge Mathematik, welche nach der einführenden Lerneinheit 401-2604-00L Wahrscheinlichkeit und Statistik (Probability and Statistics) mindestens ein Kernfach oder Wahlfach in Statistik besucht haben. Das Seminar wird auch für Studierende der Master-Studiengänge Statistik bzw. Data Science angeboten.
W4 KP2SF. Balabdaoui
KurzbeschreibungReview of some non-standard regression models and the statistical properties of estimation methods in such models.
LernzielThe main goal is the students get to discover some less known regression models which either generalize the well-known linear model (for example monotone regression) or violate some of the most fundamental assumptions (as in shuffled or unlinked regression models).
InhaltLinear regression is one of the most used models for prediction and hence one of the most understood in statistical literature. However, linearity might too simplistic to capture the actual relationship between some response and given covariates. Also, there are many real data problems where linearity is plausible but the actual pairing between the observed covariates and responses is completely lost or at partially. In this seminar, we review some of the non-classical regression models and the statistical properties of the estimation methods considered by well-known statisticians and machine learners. This will encompass:
1. Monotone regression
2. Single index model
3. Unlinked regression
4. Partially unlinked regression
SkriptNo script is necessary for this seminar
LiteraturIn the following is the material that will read and studied by each pair of students (all the items listed below are available through the ETH electronic library or arXiv):

1. Chapter 2 from the book "Nonparametric estimation under shape constraints" by P. Groeneboom and G. Jongbloed, 2014, Cambridge University Press

2. "Nonparametric shape-restricted regression" by A. Guntuoyina and B. Sen, 2018, Statistical Science, Volume 33, 568-594

3. "Asymptotic distributions for two estimators of the single index model" by Y. Xia, 2006, Econometric Theory, Volume 22, 1112-1137

4. "Least squares estimation in the monotone single index model" by F. Balabdaoui, C. Durot and H. K. Jankowski, Journal of Bernoulli, 2019, Volume 4B, 3276-3310

5. "Least angle regression" by B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, 2004, Annals of Statsitics, Volume 32, 407-499.

6. "Sharp thresholds for high dimensional and noisy sparsity recovery using l1-constrained quadratic programming (Lasso)" by M. Wainwright, 2009, IEEE transactions in Information Theory, Volume 55, 1-19

7."Denoising linear models with permuted data" by A. Pananjady, M. Wainwright and T. A. Courtade and , 2017, IEEE International Symposium on Information Theory, 446-450.

8. "Linear regression with shuffled data: statistical and computation limits of permutation recovery" by A. Pananjady, M. Wainwright and T. A. Courtade , 2018, IEEE transactions in Information Theory, Volume 64, 3286-3300

9. "Linear regression without correspondence" by D. Hsu, K. Shi and X. Sun, 2017, NIPS

10. "A pseudo-likelihood approach to linear regression with partially shuffled data" by M. Slawski, G. Diao, E. Ben-David, 2019, arXiv.

11. "Uncoupled isotonic regression via minimum Wasserstein deconvolution" by P. Rigollet and J. Weed, 2019, Information and Inference, Volume 00, 1-27
401-3900-16LAdvanced Topics in Discrete Optimization Information Belegung eingeschränkt - Details anzeigen
Number of participants limited to 12.
W4 KP2SC. Angelidakis, A. A. Kurpisz, R. Zenklusen
KurzbeschreibungIn this seminar we will discuss selected topics in discrete optimization. The main focus is on mostly recent research papers in the field of Combinatorial Optimization.
LernzielThe goal of the seminar is twofold. First, we aim at improving students' presentation and communication skills. In particular, students are to present a research paper to their peers and the instructors in a clear and understandable way. Second, students learn a selection of recent cutting-edge approaches in the field of Combinatorial Optimization by attending the other students' talks. A very active participation in the seminar helps students to build up the necessary skills for parsing and digesting advanced technical texts on a significantly higher complexity level than usual textbooks.

A key goal is that students prepare their presentations in a concise and accessible way to make sure that other participants get a clear idea of the presented results and techniques.

Students intending to do a project in optimization are strongly encouraged to participate.
InhaltThe selected topics will cover various classical and modern results in Combinatorial Optimization.

Contrary to prior years, a very significant component of the seminar will be interactive discussions where active participation of the students is required.
LiteraturThe learning material will be in the form of scientific papers.
Voraussetzungen / BesonderesRequirements: We expect students to have a thorough understanding of topics covered in the course "Mathematical Optimization".
401-3940-20LStudent Seminar in Mathematics and Data: Optimization of Random Functions Belegung eingeschränkt - Details anzeigen
Number of participants limited to 12.
W4 KP2SA. Bandeira
KurzbeschreibungMore information at course webpage:
https://people.math.ethz.ch/~abandeira/Spring2020.StudentSeminar.html
Lernziel
401-3530-20LStokes Phenomenon and Isomonodromy Equations Belegung eingeschränkt - Details anzeigen
Findet dieses Semester nicht statt.
Number of participants limited to 12.
The seminar does not take place in the Spring Semester 2020.
W4 KP2SG. Felder
KurzbeschreibungOrdinary differential equations with irregular singularities, Stokes phenomenon, isomonodromy deformations and appications.
Lernziel
InhaltThis seminar is about the study of ordinary differential equations with poles and its application in mathematical physics.
When a system of differential equations has an irregular singularity, such as a pole of order two or higher, a solution may fail to have a well-defined asymptotic expansion at the singular locus. Instead, there is a collection of angular sectors surrounding the singular locus, in each of which an asymptotic expansion is defined. The existence of such sectorial asymptotic expansions is what is called the “Stokes phenomenon”.

The Stokes phenomenon has found remarkable applications in different areas of mathematics and physics, such as in cohomological field theory, the study of stability conditions, noncommutative Hodge theory, cluster algebras, quantum groups and so on. In particular, the Stokes phenomenon is the essential ingredient in an irregular version of the Riemann-Hilbert correspondence, where the moduli space of differential equations with irregular singularities is described in terms of its associated generalized monodromy data (Stokes matrices). Moreover, the crucial role of the Stokes phenomenon in the study of representation theory and integrable systems is only beginning to emerge. The first 9 talks will include a general introduction to Stokes phenomenon and isomonodromy deformation. The last 3 talks of the seminar will focus on its applications.
LiteraturWerner Balser, Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations, Chapter 1-9, Springer.

P. Boalch, Stokes matrices, Poisson Lie groups and Frobenius manifolds, Invent. Math. 146 (2001), 479–506.

P. Boalch, G-bundles, isomonodromy and quantum Weyl groups, Int. Math. Res. Not. (2002), no. 22, 1129–1166.

B. Dubrovin, Geometry of 2d topological field theory, Lecture 1-3, https://arxiv.org/pdf/hep-th/9407018.pdf.

B. Dubrovin, Painleve transcendents in two-dimensional topological field theory, The Painleve property, Springer, New York, 1999, pp. 287–412.
252-4102-00LSeminar on Randomized Algorithms and Probabilistic Methods Belegung eingeschränkt - Details anzeigen
The deadline for deregistering expires at the end of the second week of the semester. Students who are still registered after that date, but do not attend the seminar, will officially fail the seminar.

Number of participants limited to 24.
W2 KP2SA. Steger
KurzbeschreibungThe aim of the seminar is to study papers which bring the students to the forefront of today's research topics. This semester we will study selected papers of the conference Symposium on Discrete Algorithms (SODA18).
LernzielRead papers from the forefront of today's research; learn how to give a scientific talk.
Voraussetzungen / BesonderesThe seminar is open for both students from mathematics and students from computer science. As prerequisite we require that you passed the course Randomized Algorithms and Probabilistic Methods (or equivalent, if you come from abroad).
263-4203-00LGeometry: Combinatorics and Algorithms Information
The deadline for deregistering expires at the end of the second week of the semester. Students who are still registered after that date, but do not attend the seminar, will officially fail the seminar.
W2 KP2SB. Gärtner, M. Hoffmann, E. Welzl, M. Wettstein
KurzbeschreibungThis seminar complements the course Geometry: Combinatorics & Algorithms. Students of the seminar will present original research papers, some classic and some of them very recent.
LernzielEach student is expected to read, understand, and elaborate on a selected research paper. To this end, (s)he should give a 45-min. presentation about the paper. The process includes

* getting an overview of the related literature;
* understanding and working out the background/motivation:
why and where are the questions addressed relevant?
* understanding the contents of the paper in all details;
* selecting parts suitable for the presentation;
* presenting the selected parts in such a way that an audience
with some basic background in geometry and graph theory can easily understand and appreciate it.
InhaltThis seminar is held once a year and complements the course Geometry: Combinatorics & Algorithms. Students of the seminar will present original research papers, some classic and some of them very recent. The seminar is a good preparation for a master, diploma, or semester thesis in the area.
Voraussetzungen / BesonderesPrerequisite: Successful participation in the course "Geometry: Combinatorics & Algorithms" (takes place every HS) is required.
» Seminare (Mathematik Master)
Ergänzende Fächer
kein Angebot in diesem Semester
Bachelor-Arbeit
NummerTitelTypECTSUmfangDozierende
401-2000-00LScientific Works in Mathematics
Zielpublikum:
Bachelor-Studierende im dritten Jahr;
Master-Studierende, welche noch keine entsprechende Ausbildung vorweisen können.
O0 KPÖ. Imamoglu, E. Kowalski
KurzbeschreibungIntroduction to scientific writing for students with focus on publication standards and ethical issues, especially in the case of citations (references to works of others.)
LernzielLearn the basic standards of scientific works in mathematics.
Inhalt- Types of mathematical works
- Publication standards in pure and applied mathematics
- Data handling
- Ethical issues
- Citation guidelines
SkriptMoodle of the Mathematics Library: https://moodle-app2.let.ethz.ch/course/view.php?id=519
Voraussetzungen / BesonderesDirective Link
401-2000-01LLunch Sessions – Thesis Basics für Mathematik-Studierende
Für Details und zur Registrierung für den freiwilligen MathBib-Schulungskurs: https://www.math.ethz.ch/mathbib-schulungen
Z0 KPReferent/innen
KurzbeschreibungFreiwilliger Kurs "Recherchieren in der Mathematik" angeboten von der Mathematikbibliothek.
Lernziel
401-3990-10LBachelor-Arbeit Belegung eingeschränkt - Details anzeigen
Voraussetzung: erfolgreicher Abschluss der Lerneinheit 401-2000-00L Scientific Works in Mathematics
Weitere Angaben unter www.math.ethz.ch/intranet/students/study-administration/theses.html
O8 KP11DBetreuer/innen
KurzbeschreibungDie Bachelor-Arbeit dient der Vertiefung in einem spezifischen Fachbereich; die Themen werden den Studierenden zur individuellen Auswahl angeboten. Sie soll die Fähigkeit der Studierenden zu selbständiger mathematischer Tätigkeit und zur schriftlichen Darstellung mathematischer Ergebnisse fördern.
Lernziel
GESS Wissenschaft im Kontext
Wissenschaft im Kontext
» siehe Studiengang Wissenschaft im Kontext: Typ A: Förderung allgemeiner Reflexionsfähigkeiten
» Empfehlungen aus dem Bereich Wissenschaft im Kontext (Typ B) für das D-MATH
Sprachkurse
» siehe Studiengang Wissenschaft im Kontext: Sprachkurse ETH/UZH
Zusätzliche Veranstaltungen
NummerTitelTypECTSUmfangDozierende
401-5000-00LZurich Colloquium in Mathematics Information E-0 KPR. Abgrall, P. L. Bühlmann, M. Iacobelli, A. Iozzi, S. Mishra, R. Pandharipande, weitere Dozierende
KurzbeschreibungThe lectures try to give an overview of "what is going on" in important areas of contemporary mathematics, to a wider non-specialised audience of mathematicians.
Lernziel
401-5990-00LZurich Graduate Colloquium Information E-0 KPA. Iozzi, Uni-Dozierende
KurzbeschreibungThe Graduate Colloquium is an informal seminar aimed at graduate students and postdocs whose purpose is to provide a forum for communicating one's interests and thoughts in mathematics.
Lernziel
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