Emmanuel Kowalski: Katalogdaten im Herbstsemester 2018 |
| Name | Herr Prof. Dr. Emmanuel Kowalski |
| Lehrgebiet | Mathematik |
| Adresse | Professur für Mathematik ETH Zürich, HG G 64.1 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telefon | +41 44 632 34 41 |
| emmanuel.kowalski@math.ethz.ch | |
| URL | http://www.math.ethz.ch/~kowalski |
| Departement | Mathematik |
| Beziehung | Ordentlicher Professor |
| Nummer | Titel | ECTS | Umfang | Dozierende | |
|---|---|---|---|---|---|
| 401-0213-16L | Analysis II  | 5 KP | 2V + 2U | E. Kowalski | |
| Kurzbeschreibung | Differential and Integral calculus in many variables, vector analysis. | ||||
| Lernziel | Differential and Integral calculus in many variables, vector analysis. | ||||
| Inhalt | Differential and Integral calculus in many variables, vector analysis. | ||||
| Literatur | Für allgemeine Informationen, sehen Sie bitte die Webseite der Vorlesung: https://metaphor.ethz.ch/x/2017/hs/401-0213-16L/ | ||||
| 401-2000-00L | Scientific Works in Mathematics Zielpublikum: Bachelor-Studierende im dritten Jahr; Master-Studierende, welche noch keine entsprechende Ausbildung vorweisen können. | 0 KP | E. Kowalski | ||
| Kurzbeschreibung | Introduction to scientific writing for students with focus on publication standards and ethical issues, especially in the case of citations (references to works of others.) | ||||
| Lernziel | Learn 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 | ||||
| Skript | Moodle of the Mathematics Library: https://moodle-app2.let.ethz.ch/course/view.php?id=519 | ||||
| Voraussetzungen / Besonderes | Weisung https://www.ethz.ch/content/dam/ethz/common/docs/weisungssammlung/files-de/wiss-arbeiten-eigenst%C3%A4ndigkeitserklaerung.pdf | ||||
| 401-3113-68L | Exponential Sums over Finite Fields | 8 KP | 4G | E. Kowalski | |
| Kurzbeschreibung | Exponential sums over finite fields arise in many problems of number theory. We will discuss the elementary aspects of the theory (centered on the Riemann Hypothesis for curves, following Stepanov's method) and survey the formalism arising from Deligne's general form of the Riemann Hypothesis over finite fields. We will then discuss various applications, especially in analytic number theory. | ||||
| Lernziel | The goal is to understand both the basic results on exponential sums in one variable, and the general formalism of Deligne and Katz that underlies estimates for much more general types of exponential sums, including the "trace functions" over finite fields. | ||||
| Inhalt | Examples of elementary exponential sums The Riemann Hypothesis for curves and its applications Definition of trace functions over finite fields The formalism of the Riemann Hypothesis of Deligne Selected applications | ||||
| Skript | Lectures notes from various sources will be provided | ||||
| Literatur | Kowalski, "Exponential sums over finite fields, I: elementary methods: Iwaniec-Kowalski, "Analytic number theory", chapter 11 Fouvry, Kowalski and Michel, "Trace functions over finite fields and their applications" | ||||
| 401-5110-00L | Number Theory Seminar | 0 KP | 1K | Ö. Imamoglu, P. S. Jossen, E. Kowalski, P. D. Nelson, R. Pink, G. Wüstholz | |
| Kurzbeschreibung | Research colloquium | ||||
| Lernziel | |||||
| 406-2005-AAL | Algebra I and II Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben. Alle andere Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen. | 12 KP | 26R | M. Burger, E. Kowalski | |
| Kurzbeschreibung | Introduction and development of some basic algebraic structures - groups, rings, fields including Galois theory, representations of finite groups, algebras. The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. | ||||
| Lernziel | |||||
| Inhalt | Basic notions and examples of groups; Subgroups, Quotient groups and Homomorphisms, Group actions and applications Basic notions and examples of rings; Ring Homomorphisms, ideals, and quotient rings, rings of fractions Euclidean domains, Principal ideal domains, Unique factorization domains Basic notions and examples of fields; Field extensions, Algebraic extensions, Classical straight edge and compass constructions Fundamentals of Galois theory Representation theory of finite groups and algebras | ||||
| Skript | For a summary of the content and exercises with solutions of my lecture courses in HS2015 and FS2016 see: https://www2.math.ethz.ch/education/bachelor/lectures/hs2015/math/algebra1/index-2.html https://www2.math.ethz.ch/education/bachelor/lectures/fs2016/math/algebra2/ | ||||
| Literatur | S. Lang, Algebra, Springer Verlag B.L. van der Waerden: Algebra I und II, Springer Verlag I.R. Shafarevich, Basic notions of algebra, Springer verlag G. Mislin: Algebra I, vdf Hochschulverlag U. Stammbach: Algebra, in der Polybuchhandlung erhältlich I. Stewart: Galois Theory, Chapman Hall (2008) G. Wüstholz, Algebra, vieweg-Verlag, 2004 J-P. Serre, Linear representations of finite groups, Springer Verlag | ||||