Extremal Combinatorics in Random Discrete Structures 
February 27 - March 23, 2012
Lectures:   Mon-Fri, 9:00-12:00
Exercises:  Tue-Fri, 16:00-18:00
Freie Universität Berlin

1. Extremal Combinatorics and the Probabilistic Method -- an Introduction (Tibor Szabo, FU Berlin)
    February 27-March 2, 2012

2. Multiple Round Exposure in Random Structures (Mathias Schacht, University of Hamburg)
    March 5-9 and March 12-16, 2012

3. Transference Principles (David Conlon, University of Oxford)
    March 15-16 and March 19-23, 2012

Abstract:
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.

More information: http://www3.math.tu-berlin.de/MDS/blockcourse12.html