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
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
Dragana Radojičić, BMS Alumna, MSc TU Berlin, Qualifying Exam BMS, BSc University of Belgrade
Alexander Fairley, BMS Phase II student,Qualifying Exam BMS, BSc University of Glasgow
Efstathia Katsigianni, BMS Phase II Student, MSc HU Berlin, Qualifying Exam BMS, BSc University of Patras
Christoph Gorgulla, BMS Alumnus, PhD completed in May 2018, MSc Freie Universität Berlin, BSc Freie Universität Berlin
Ignacio Barros, BMS Alumnus, PhD completed in June 2018, Qualifying Exam BMS, MSc Freie Universität Berlin, BSc Pontific...
Todor Bilarev, BMS Phase II Student, Qualifying Exam BMS, MSc Humboldt-Universität zu Berlin, BSc Jacobs University Brem...
Tanya Kaushal Srivastava, Phase II student, MSc Indian Institute of Science and Education and research (IISER) Mohali, P...
Josué Tonelli Cueto, BMS Phase II Student, Qualifying Exam BMS, MSc Technische Universität Berlin, BSc University of the...
Hector Andrade Loarca, BMS Phase I student, BSc National Autonomous University of Mexico
Block Course with Conlon, Schacht and Szabo