# Suchergebnis: Katalogdaten im Herbstsemester 2021

Mathematik Bachelor | ||||||

Seminare ZUR BEACHTUNG: Damit die Zuteilung der verfügbaren Seminarplätze sich nicht primär auf den Zeitpunkt des Einschreibens in die Warteliste stützen muss, haben die Mathematik-Seminare ein spezielles Auswahlverfahren. Eine direkte Belegung in myStudies ist nicht möglich, alle kommen zuerst auf die Warteliste. Ausserdem gilt: Die Auswahl an Mathematik-Seminaren wird auf 1 Seminar pro Semester beschränkt. | ||||||

Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
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401-3050-71L | Student Seminar in Combinatorics Number of participants limited to 12. | W | 4 KP | 2S | B. Sudakov | |

Kurzbeschreibung | The seminar will consist of student presentations and will cover a variety of topics in modern-day combinatorics. The seminar is aimed at third year bachelor students or master students with a background in combinatorics (e.g. the Graph Theory course). | |||||

Lernziel | The seminar's aim is to acquaint students with interesting results, proofs and techniques in combinatorics and graph theory, and to give them the opportunity to work with advanced research papers and practice their presentation skills. | |||||

401-3110-71L | Student Seminar in Elementary Number Theory Number of participants limited to 22. | W | 4 KP | 2S | Ö. Imamoglu | |

Kurzbeschreibung | This is a student seminar covering a range of topics in elementary number theory. | |||||

Lernziel | The purpose of this seminar is to introduce a diversified range of topics in elementary number theory, each of which has spurred, and still motivates, a great deal of research in the area. This will hopefully encourage a deeper understanding of the subject and serve as a basis for more advanced courses. | |||||

Literatur | An introduction to the theory of numbers (5th edition) by G.H. Hardy and E.M. Wright (Oxford University Press 1980) Introduction to Analytic Number Theory by T.M. Apostol (Springer 1976) Introduction to Analytic Number Theory by K. Chandrasekharan (Springer 1968) | |||||

Voraussetzungen / Besonderes | Funktion theory and Algebra I & II are prerequisites. | |||||

401-3100-71L | Student Seminar in Number Theory: L-Functions Number of participants limited to 24. | W | 4 KP | 2S | M. Schwagenscheidt | |

Kurzbeschreibung | Seminar on the basic theory of Dirichlet L-functions and some applications in number theory. | |||||

Lernziel | In the seminar we will study Dirichlet L-functions, which generalize the classical Riemann zeta function. We discuss their basic properties, such as the analytic continuation and the functional equation, and the rationality of some of their special values. Moreover, we investigate the connection of Dirichlet L-functions with the Dedekind zeta functions of quadratic number fields. As main applications, we prove Dirichlet's class number formula for quadratic fields and Dirichlet's Theorem on arithmetic progressions. We follow the book of Don Zagier "Zetafunktionen und quadratische Körper" | |||||

Inhalt | Please see the website of the seminar for a list of topics: https://people.math.ethz.ch/~mschwagen/lfunctions | |||||

Literatur | Apostol - Introduction to analytic number theory Davenport - Multiplicative number theory Serre - A course in arithmetic Zagier - Zetafunktionen und quadratische Körper | |||||

Voraussetzungen / Besonderes | Some familiarity with the basic notions of algebra (groups, rings, fields), complex analysis (holomorphic/meromorphic functions, the residue theorem) and elementary number theory (congruences, Legendre symbol, quadratic reciprocity) will be helpful. | |||||

401-3550-71L | Student Seminar in Topological Data Analysis Number of participants limited to 12. | W | 4 KP | 2S | S. Kalisnik Hintz | |

Kurzbeschreibung | In this seminar we will learn about the standard tools in topological data analysis. They are drawn from classical topology and focus on the shape of data in one of two ways: they either `measure’ it, that is count the occurrences of patterns within the data set; or build combinatorial representations of the data set. An example of the former is persistent homology, whereas of the latter, mapper. | |||||

Lernziel | ||||||

Inhalt | In this seminar we will learn about the standard tools in topological data analysis. They are drawn from classical topology and focus on the shape of data in one of two ways: they either `measure’ it, that is count the occurrences of patterns within the data set; or build combinatorial representations of the data set. An example of the former is persistent homology, whereas of the latter, mapper. We will also take a look at some applications of both. | |||||

Literatur | -Topological pattern recognition for point cloud data, G. Carlsson, Acta Numerica, Volume 23 , May 2014 , pp. 289 - 368 -Computational Topology: an Introduction, H. Edelsbrunner, J. Harer, American Mathematical Soc. -H. Adams, A. Tausz, Javaplex tutorial (2018), http://appliedtopology.github.io/javaplex/ -On the local behavior of spaces of natural images, G. Carlsson, T. Ishkhanov, V. De Silva, A. Zomorodian, International journal of computer vision 76 (1), 1-12. -Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition, G. Singh, F. Memoli, G. Carlsson, Point Based Graphics 2007 -Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival, M. Nicolau, A.J. Levine, G. Carlsson, Proceedings of the National Academy of Sciences 108 (17), 7265-7270 -Zigzag persistence, G. Carlsson, V. De Silva, Foundations of computational mathematics 10 (4), 367-405 | |||||

401-3140-71L | Student Seminar in Algebraic Geometry: Complex Algebraic Surfaces Number of participants limited to 12. | W | 4 KP | 2S | T.‑H. Bülles, R. Pandharipande | |

Kurzbeschreibung | The aim of the seminar is to understand the Enriques classification of complex algebraic surfaces. | |||||

Lernziel | We will see how techniques of algebraic geometry are applied to classify complex algebraic surfaces. Along the way we discuss invariants from cohomology and intersection theory and encounter important examples of varieties, such as ruled, abelian and K3 surfaces. | |||||

Voraussetzungen / Besonderes | We assume familiarity with the basic concepts of Algebraic Geometry, roughly in the amount of chapters II and III of Hartshorne’s book. | |||||

401-3940-71L | Student Seminar in Mathematics and Data: Stochastic Optimization Number of participants limited to 12. | W | 4 KP | 2S | A. Bandeira, G. Chinot, N. Zhivotovskii | |

Kurzbeschreibung | ||||||

Lernziel | ||||||

401-3620-20L | Student Seminar in Statistics: Inference in Some Non-Standard Regression Problems 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. | W | 4 KP | 2S | F. Balabdaoui | |

Kurzbeschreibung | Review of some non-standard regression models and the statistical properties of estimation methods in such models. | |||||

Lernziel | The 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). | |||||

Inhalt | Linear regression is one of the most used models for prediction and hence one of the most understood in statistical literature. However, linearity might be 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 | |||||

Literatur | In the following is the tentative material that will be read and studied by each pair of students (all the items listed below are available through the ETH electronic library or arXiv). Some of the items might change. 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 | |||||

Voraussetzungen / Besonderes | The students need to be comfortable with regression models, classical estimation methods (Least squares, Maximum Likelihood estimation...), rates of convergence, asymptotic normality, etc. | |||||

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