Advances in Extremal Combinatorics

Master's Seminar in Discrete Mathematics

Winter 2019-20

FU Berlin, Mathematics and Informatics



Topics

This seminar continues along the lines of the Discrete Mathematics course sequence. We will cover a number of (relatively) recent breakthroughs from various areas of combinatorics.

References

A list of topics, which will be added to in the coming weeks, is given below. Included are links to some source material, from which you should prepare your talks. You should also feel free to read around the topic and find other references that may be of use.

To begin with, please take a look at these papers. We will assign topics and set the seminar schedule during our initial meeting on October 15th. In case you cannot make this meeting because of a clash with another course, please send us an e-mail in advance letting us know which topics you are interested in. Please also tell us what times you would be free for the seminar, as we will try to reschedule it to a convenient time if there are a lot of clashes.

Topic Adviser Source material
The Combinatorial Nullstellensatz and applications Tibor Alon
The List Colouring Conjecture Tibor Häggkvist-Janssen;
Schauz
The sensitivity conjecture Shagnik Chung-Füredi-Graham-Seymour;
Huang
Cliques in Paley graphs Tibor Hanson-Petridis
Erdős-Ginzburg-Ziv and the Kemnitz Conjecture Shagnik Rónyai;
Sauermann
The Erdős Sunflower Conjecture Shagnik Alweiss-Lovett-Wu-Zhang;
Rao
Enumerating independent sets Shagnik Kahn-Park;
Kahn;
Zhao
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Course Details

Instructor

The seminar will be run by

Tibor Szabó
Arnimallee 3, Rm 211a
szabo at math dot fu-berlin dot de

Prerequisites

A general prerequisite is familiarity with combinatorics.

A formal prerequisite is the successful completion of the Finite Geometry (Discrete Mathematics III) course taught in the Summer 2019 semester, or the consent of the instructor (please contact if necessary).

Credits

This course can be used as a Vertiefungsmodul or an Ergänzungsmodul in the Masters curriculum of the Freie Universität, or as an advanced seminar course in the curriculum of the Berlin Mathematical School.

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Schedule

The seminar will take place on Tuesdays, 10:15 to 11:45 in Arnimallee 3, SR 119.

Date Speaker Title
Oct 15 Tibor Assignment of talks
Nov 12 Krisztina The Combinatorial Nullstellensatz
Nov 19 Yizhou The List Colouring Conjecture I
Nov 26 Alp The List Colouring Conjecture II
Dec 3 Matthias The Sensitivity Conjecture
Dec 10 Felipe/Matteo Cliques in Paley graphs I
Dec 17 Felipe/Matteo Cliques in Paley graphs II
Jan 7 Ander/Simona Erdős-Ginzburg-Ziv and the Kemnitz Conjecture I
Jan 14 Ander/Simona Erdős-Ginzburg-Ziv and the Kemnitz Conjecture II
Jan 21 Adam The Erdős Sunflower Conjecture
Jan 28 Thomas Enumerating independent sets
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