## Benjamin Sudakov: Catalogue data in Autumn Semester 2022 |

Name | Prof. Dr. Benjamin Sudakov |

Field | Mathematics |

Address | Institut für Operations Research ETH Zürich, HG G 65.1 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 40 28 |

benjamin.sudakov@math.ethz.ch | |

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

Department | Mathematics |

Relationship | Full Professor |

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

252-4202-00L | Seminar in Theoretical Computer Science | 2 credits | 2S | E. Welzl, B. Gärtner, M. Hoffmann, J. Lengler, A. Steger, D. Steurer, B. Sudakov | |

Abstract | Presentation of recent publications in theoretical computer science, including results by diploma, masters and doctoral candidates. | ||||

Learning objective | The goal is to introduce students to current research, and to enable them to read, understand, and present scientific papers. | ||||

Prerequisites / Notice | This seminar takes place as part of the joint research seminar of several theory groups. Intended participation is for students with excellent performance only. Formal restriction is: prior successful participation in a master level seminar in theoretical computer science. | ||||

401-3050-72L | Student Seminar in Combinatorics Number of participants limited to 12. | 4 credits | 2S | B. Sudakov | |

Abstract | 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). | ||||

Learning objective | 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. | ||||

401-3054-DRL | Probabilistic Methods in Combinatorics Only for ZGSM (ETH D-MATH and UZH I-MATH) doctoral students. The latter need to register at myStudies and then send an email to info@zgsm.ch with their name, course number and student ID. Please see https://zgsm.math.uzh.ch/index.php?id=forum0 | 2 credits | 2V + 1U | B. Sudakov | |

Abstract | This course provides a gentle introduction to the Probabilistic Method, with an emphasis on methodology. We will try to illustrate the main ideas by showing the application of probabilistic reasoning to various combinatorial problems. | ||||

Learning objective | |||||

Content | The topics covered in the class will include (but are not limited to): linearity of expectation, the second moment method, the local lemma, correlation inequalities, martingales, large deviation inequalities, Janson and Talagrand inequalities and pseudo-randomness. | ||||

Literature | - The Probabilistic Method, by N. Alon and J. H. Spencer, 3rd Edition, Wiley, 2008. - Random Graphs, by B. Bollobás, 2nd Edition, Cambridge University Press, 2001. - Random Graphs, by S. Janson, T. Luczak and A. Rucinski, Wiley, 2000. - Graph Coloring and the Probabilistic Method, by M. Molloy and B. Reed, Springer, 2002. | ||||

401-3054-14L | Probabilistic Methods in Combinatorics | 6 credits | 2V + 1U | B. Sudakov | |

Abstract | This course provides a gentle introduction to the Probabilistic Method, with an emphasis on methodology. We will try to illustrate the main ideas by showing the application of probabilistic reasoning to various combinatorial problems. | ||||

Learning objective | |||||

Content | The topics covered in the class will include (but are not limited to): linearity of expectation, the second moment method, the local lemma, correlation inequalities, martingales, large deviation inequalities, Janson and Talagrand inequalities and pseudo-randomness. | ||||

Literature | - The Probabilistic Method, by N. Alon and J. H. Spencer, 3rd Edition, Wiley, 2008. - Random Graphs, by B. Bollobás, 2nd Edition, Cambridge University Press, 2001. - Random Graphs, by S. Janson, T. Luczak and A. Rucinski, Wiley, 2000. - Graph Coloring and the Probabilistic Method, by M. Molloy and B. Reed, Springer, 2002. | ||||

401-3055-64L | Algebraic Methods in Combinatorics Does not take place this semester. | 6 credits | 2V + 1U | B. Sudakov | |

Abstract | Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. This course provides a gentle introduction to Algebraic methods, illustrated by examples and focusing on basic ideas and connections to other areas. | ||||

Learning objective | The students will get an overview of various algebraic methods for solving combinatorial problems. We expect them to understand the proof techniques and to use them autonomously on related problems. | ||||

Content | Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. While in the past many of the basic combinatorial results were obtained mainly by ingenuity and detailed reasoning, the modern theory has grown out of this early stage and often relies on deep, well-developed tools. One of the main general techniques that played a crucial role in the development of Combinatorics was the application of algebraic methods. The most fruitful such tool is the dimension argument. Roughly speaking, the method can be described as follows. In order to bound the cardinality of of a discrete structure A one maps its elements to vectors in a linear space, and shows that the set A is mapped to linearly independent vectors. It then follows that the cardinality of A is bounded by the dimension of the corresponding linear space. This simple idea is surprisingly powerful and has many famous applications. This course provides a gentle introduction to Algebraic methods, illustrated by examples and focusing on basic ideas and connections to other areas. The topics covered in the class will include (but are not limited to): Basic dimension arguments, Spaces of polynomials and tensor product methods, Eigenvalues of graphs and their application, the Combinatorial Nullstellensatz and the Chevalley-Warning theorem. Applications such as: Solution of Kakeya problem in finite fields, counterexample to Borsuk's conjecture, chromatic number of the unit distance graph of Euclidean space, explicit constructions of Ramsey graphs and many others. The course website can be found at https://moodle-app2.let.ethz.ch/course/view.php?id=15757 | ||||

Lecture notes | Lectures will be on the blackboard only, but there will be a set of typeset lecture notes which follow the class closely. | ||||

Prerequisites / Notice | Students are expected to have a mathematical background and should be able to write rigorous proofs. |