This seminar is an introduction to extremal set theory - a fast-growing field of discrete mathematics, which investigates questions of the following type: if we have a collection of sets satisfying certain restrictions, how large or how small can it be?

The seminar is held in English.

### How to find us

The seminar room K2 is within the **building 01.93** located in **Kronenplatz 32**. You can find it on this map in square D9. When standing on Kronenplatz look for a travel agency called "Reiseland" and for the entrance left of it. The door is usually locked but there is a door bell at the panel labeled **KIT Mathematik Seminarraum**. Ring that bell and wait for someone to open.

### News

**From now on the preliminary meeting (unless otherwise agreed) will take place on Tuesdays from 10:00am to 11:00am!**

# Content

The seminar will cover **'Part II. Extremal Set Theory**' and **'Part III. The Linear Algebra Method**' of the book **"Extremal Combinatorics"** by Stasys Jukna.

The book is available as online ressource within the KIT network.

# Format

Each week one student presents a chapter or part of a chapter of the book at the blackboard. Presentations should be self-contained, assuming only basic mathematical knowledge and the content of the preceeding chapters.

Students need to meet with a lecturer (either Prof. Maria Axenovich or Torsten Ueckerdt) **the week before** their presentation. The student's presentation should be set up by then, so that lecturer and student can go through the material together and clarify remaining questions.

The default setting is a meeting with Torsten on Tuesday at **10:00am** in his office room A4-01 Allianz-Gebäude. Deviation from that time and place only on mutual agreement.

# Tentative Schedule

Note that the numbering of chapters and sections used below is taken from the 2nd edition (2011) of Jukna's book. This is the edition available as online ressource and linked above.

**date** | **name** | **chapter** | **sections** |

Oct. 16 | Prof. Maria Axenovich | Introduction |

Oct. 23 | Jonathan R. | Sunflowers | 6.1-6.3 |

Oct. 30 | Dominique K. | Intersecting Families | 7.1-7.5 |

Nov. 6 | Fabian S. | Chains and Antichains | 8.1-8.6 |

Nov. 13 | Lisa K. | Blocking Sets and the Duality | 9.1-9.5 |

Nov. 20 | Torsten | Density and Universality | 10.1-10.7 |

Nov. 27 | Johannes L. | Witness Sets and Isolation | 11.1-11.4 |

Dec. 4 | Franz K. | Designs | 12.1-12.5 |

Dec. 11 | Daniel K. | The Basic Method | 13.1-13.8 |

Dec. 18 | Daniel H. | Orthogonality and Rank Arguments | 14.1-14.5 |

Jan. 15 | Dirk T. | Eigenvalues and Graph Expansions | 15.1-15.3 |

Jan. 22 | Joanne V. | The Polynomial Method | 16.1-16.3 |

Jan. 29 | Stefan W. | Combinatorics of Codes | 17.1-17.7 |

Feb. 5 | Torsten | The Kruskal Katona Theorem | 10.4 |

In case of any questions concerning the course of the seminar or the presentations itself, please do not hesitate to contact us!

Prof. Maria Axenovich Ph.D.

Torsten Ueckerdt

last update: December 19, 2012