## Emmanuel Kowalski: Catalogue data in Spring Semester 2020 |

Name | Prof. Dr. Emmanuel Kowalski |

Field | Mathematics |

Address | Professur für Mathematik ETH Zürich, HG G 64.1 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 34 41 |

emmanuel.kowalski@math.ethz.ch | |

URL | http://www.math.ethz.ch/~kowalski |

Department | Mathematics |

Relationship | Full Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-2000-00L | Scientific Works in MathematicsTarget audience: Third year Bachelor students; Master students who cannot document to have received an adequate training in working scientifically. | 0 credits | Ö. Imamoglu, E. Kowalski | ||

Abstract | 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.) | ||||

Objective | Learn the basic standards of scientific works in mathematics. | ||||

Content | - Types of mathematical works - Publication standards in pure and applied mathematics - Data handling - Ethical issues - Citation guidelines | ||||

Lecture notes | Moodle of the Mathematics Library: https://moodle-app2.let.ethz.ch/course/view.php?id=519 | ||||

Prerequisites / Notice | Directive https://www.ethz.ch/content/dam/ethz/common/docs/weisungssammlung/files-en/declaration-of-originality.pdf | ||||

401-3109-65L | Probabilistic Number Theory Does not take place this semester. | 8 credits | 4G | E. Kowalski | |

Abstract | The course presents some results of probabilistic number theory in a unified manner, including distribution properties of the number of prime divisors of integers, probabilistic properties of the zeta function and statistical distribution of exponential sums. | ||||

Objective | The goal of the course is to present some results of probabilistic number theory in a unified manner. | ||||

Content | The main concepts will be presented in parallel with the proof of a few main theorems: (1) the Erdős-Wintner and Erdős-Kac theorems concerning the distribution of values of arithmetic functions; (2) the distribution of values of the Riemann zeta function, including Selberg's central limit theorem for the Riemann zeta function on the critical line; (3) the Chebychev bias for primes in arithmetic progressions; (4) functional limit theorems for the paths of partial sums of families of exponential sums. | ||||

Lecture notes | The lecture notes for the class are available at https://www.math.ethz.ch/~kowalski/probabilistic-number-theory.pdf | ||||

Prerequisites / Notice | Prerequisites: Complex analysis, measure and integral; some probability theory is useful but the main concepts needed will be recalled. Some knowledge of number theory is useful but the main results will be summarized. | ||||

401-5110-00L | Number Theory Seminar | 0 credits | 1K | Ö. Imamoglu, P. S. Jossen, E. Kowalski, P. D. Nelson, R. Pink, G. Wüstholz | |

Abstract | Research colloquium | ||||

Objective | Talks on various topics of current research. | ||||

Content | Research seminar in algebra, number theory and geometry. This seminar is aimed in particular to members of the research groups in these areas and their graduate students. |