## Emmanuel Kowalski: Catalogue data in Autumn Semester 2010 |

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 | |
---|---|---|---|---|---|

401-0131-00L | Linear Algebra | 7 credits | 4V + 2U | E. Kowalski, M. Pollefeys | |

Abstract | Application oriented introduction to linear algebra (vector spaces, linear transformations, matrices) , matrix decompositions (LU, QR, eigenvalue, and singular value decomposition). Introduction to the programming environment Matlab. | ||||

Learning objective | |||||

Content | Linear Algebra: Linear systems of equations, vectors and matrices, norms and scalar products, LU decomposition, vector spaces and linear transformations, least squares problems, QR decomposition, determinants, eigenvalues and eigenvectors, singular value decomposition, applications. | ||||

Lecture notes | Lecture notes "Linear Algebra" (Gutknecht) in German, with English expressions for all technical terms. | ||||

Prerequisites / Notice | The relevant high school material is reviewed briefly at the beginning. | ||||

401-3127-60L | Exponential Sums over Finite Fields II | 4 credits | 2V | E. Kowalski | |

Abstract | This course presents the modern techniques, based on algebraic geometry, that are used to study exponential sums over finite fields. Although some basic statements are taken for granted, like Deligne's statement of the Riemann Hypothesis over finite fields, many applications of the formalism are presented in detail, with particular emphasis on Deligne's Equidistribution Theorem. | ||||

Learning objective | |||||

Content | This course will present the modern techniques, based on algebraic geometry, that are used to study exponential sums over finite fields. Because of the large amount of material involved, a number of important facts will be taken as "black boxes", including Deligne's statement of the general form of the Riemann Hypothesis over finite fields. However, the way to use this formalism will be explained in detail, with a particular emphasis on Deligne's Equidistribution Theorem. Various applications will be given, including bounds for multi-variable character sums, families of exponential sums, and certain sieve problems. Although this course continues the one given in the Spring Semester, the material will be quite independent, and new students should be able to follow by referring to the notes from that course. | ||||

Lecture notes | Notes will be prepared for the course. Information can already be obtained from http://www.math.ethz.ch/~kowalski/exp-sums.html | ||||

Prerequisites / Notice | Although this course continues the one given in the Spring Semester, the material will be quite independent, and new students should be able to follow by referring to the notes from that course. | ||||

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

Abstract | Research colloquium | ||||

Learning objective | |||||

401-5550-00L | Algebra-Topology Seminar | 0 credits | 1K | K. U. Baur, A. Iozzi, E. Kowalski | |

Abstract | Research colloquium | ||||

Learning objective |