Block Course – Towards the Polynomial Freiman-Ruzsa Conjecture
October 6 – 24 2014
Freie Universität Berlin
Topics and lecturers
Week 1: Giorgis
of Rochester): Classical
and new results in Additive Combinatorics
6 - 10 October 2014
Material: elementary inequalities in Additive Combinatorics (Ruzsa's triangle inequality), Plünnecke's inequality via Petridis proof, covering lemmas, Ruzsa's power trick, Additive energy and Balog-Szemerédi-Gowers Theorem, Freiman isomorphisms, sum-product estimates and Szemerédi-Trotter Theorem .
Handout 1, Handout 2, Handout 3, Handout 4, the full material and the Problems
Week 2: Julia
of Bristol): Analytic
techniques in Additive Combinatorics
13 - 16 October 2014
Material: introduction to the discrete Fourier transform and Bogolyubov’s Lemma, Meshulam’s Theorem, Croot-Sisask almost periodicity, applications including log-bound in Bogolyubov (finite fields), Roth’s theorem in the integers, Bohr sets and the notion of regularity with applications, introduction to higher-order uniformity
Week 3: Tomasz
Mickiewicz University): The
Polynomial Freiman-Ruzsa Conjecture
20 - 23 October 2014
Material: proof of Freiman Theorem (including some geometry of numbers, if needed, but it can be avoided even in the integers), Chang's spectral lemma, Schoen's attack on PFR, log-bound in Bogolyubov in the integers according to Sanders and Sanders attack (log-bound), consequences of effective bounds, new bound for size of sets without solution to a+b+c+d+e=5f (finite fields setting).
The precise schedule(lecture rooms, timetable, ...) of the Block Course
One of the first results in Additive Combinatorics is the so-called Freiman-Ruzsa Theorem, which states that a set with small sumset is in fact a subset of a generalized arithmetic progression. This theorem has emerged as an important cornerstone of the field, and many related questions are still unknown.
The course is intended for master students, PhD-students and postdoctoral researchers interested in the field of Additive Combinatorics and related areas. The course will start with a swift introduction to the classical results on the area (Week 1). Later, on Week 2, the course will move to Fourier Analytic techniques and applications in Additive Combinatorics. Finally, in Week 3, Freiman-Ruzsa Theorem and the latest achievements towards the Polynomial Freiman-Ruzsa Conjecture will be discussed.
Participants can join any part of the course, depending on their individual background and interest.
The course is addressed to graduate students and postdocs of Mathematics or Computer Science, who are interested in additive combinatorics, applications of Fourier analysis in discrete mathematics, and related fields.
The Block Course is organized within the Research Training Group "Methods for Discrete Structures” and organized by Jun. Prof. Juanjo Rué and Prof. Tibor Szabó.
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 June 30, 2014, preferably by email, to Jun. Prof. Juanjo Rué at jrue (at) zedat.fu-berlin.de
Through the generous support of the Department of Mathematics and Computer Science of Freie Universität Berlin and the Research Training Group "Methods for Discrete Structures”, 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 May 31, 2014, preferably by e-mail, to Jun. Prof. Juanjo Rué at jrue (at) zedat.fu-berlin.de
This is the place where you find hints on how to find reasonably priced accomodation, how to get around Berlin, and the like. If there is anything missing, let us know. (Some of the links lead to German pages, sorry).
There are various moderately priced housing possibilities in Berlin. Below we provide a list of hostels. It never hurts to ask if they have better conditions for longer stays than the listed per-day prices.
Another possibility with a very good price/comfort ratio is to rent a furnished appartment with a group of people. Below is a list of links where you can start your search for an appartment.