Reading Seminar on Polynomial Freiman Ruzsa (PFR)

This reading group will cover the recent breakthrough solving Marton's conjecture (also known as the Polynomial Freiman Ruzsa (PFR) Conjecture). The conjecture is a cornerstone in Additive Combinatorics and asserts that one can deduce strong structural information about a set that has bounded doubling. The resolution was achieved by Gowers, Green, Manners and Tao using a translation of the problem that utilises entropy. We will cover this proof as well as the relevant context and tools that are used.

We will meet in Room C3-005 at Campus Nord (usual seminar room) on Thursdays at 14.30. Talks will be planned to be 1 hour with space for questions and discussion after. 

Provisional Schedule:

1. Thursday 29th February: Introduction to topic, statement of theorem and discussion of some classical tools (Oriol Serra)
2. Thursday 7th March: Entropy methods, definition and basic properties of entropic Ruzsa distance, entropic formulation of PFR  (Clément Requilé)
3. Thursday 14th March: More entropy: proof that 'entropic PFR' implies 'PFR', Covering lemma, and possibly Balog–Szemerédi–Gowers lemma (Miquel Ortega)
4. Thursday 21st March: Balog–Szemerédi–Gowers lemma. Classical version and implications/context. Entropic version with proof. (Tássio Naia)
5. Thursday 11th April: Proof of PFR conjecture - big picture and scheme of proof. Fibring Lemma. (Miquel Ortega)
6. Thursday 18th April: Outline of cases with one in detail. Endgame.  (Patrick Morris)