Lectures: Mon-Fri, 9:00-12:00 Exercises: Tue-Fri, 16:00-18:00
Several classical theorems of combinatorics, such as Turán's theorem, Ramsey's theorem and Szemerédi's theorem, are known to have analogues within sparse random structures. While numerous special cases have been proved over the last twenty years, most notably by Łuczak, Kohayakawa, Rödl and Ruciński, a general treatment giving tight thresholds in all such cases was only obtained very recently. Surprisingly, there are now two very different-looking approaches to doing this, one obtained by Mathias Schacht, the other independently by David Conlon and Tim Gowers. The goal of the course is to see these two approaches next to each other and to compare them, concentrating on their analogies and differences. The plan is to understand the fundamentals and basic ideas of both approaches and fully grasp the proof of at least one special case each, together with a believable notion of how to extend them to their full generality. The course is intended for PhD-students and postdocs interested in the field of Extremal and Probabilistic Combinatorics and related areas. The course will start with a swift introduction to the classical theorems and basic probabilistic techniques. This will lead on to a discussion of techniques that have been used in the past to address problems of this variety, indicating why they cannot be used in the general case. The course will conclude with a thorough discussion of the modern developments given by the authors themselves. Students may choose to join the course at any stage, depending on their individual strengths and interests.
The course is addressed to graduate students and postdocs of Mathematics or Computer Science, who are interested in extremal combinatorics, the theory of random graphs, probabilistic methods and related fields.
A typical day will consist of a morning lecture (9:00-12:00) and an exercise session in the afternoon (16:00-18:00). The exercises are to be solved in small groups in the afternoon and will later be discussed in the exercise session. The language of the course is English.
Applications for participation in the course (the whole or part of it -- please indicate the weeks you plan to participate in), with a short curriculum vitae and scientific background, should be sent by Sept 30, 2011, preferably by email, to Ms Barrett
There is a limited amount of financial support available for PhD-students
or for advanced Master/Diploma students in a field related to the topics
of the course. Applications for financial support, with curriculum vitae,
copies of certificates, thesis, areas of interest, and a letter of
recommendation (sent directly by the letter writer) should be sent by
Sept 30, 2011, preferably by email, to Ms Barrett at
barrett (at) math.fu-berlin.de
Applicants will be notified by Oct 15, 2011.
If there are still places available, the deadline can be extended.
The Block Course is organized as part of the Research Training Group "Methods for Discrete Structures" of the Free University, the Humboldt University and the Technical University in Berlin, and organized by Tibor Szabo.