Lecture 11/23/09 — Bourgain-Glibichuk-Koryagin (part 2), additive/multiplicative Balog-Szemeredi-Gowers theorem, Bourgain-Katz-Tao theorem

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• Last lecture for Fall 2009

Lecture 11/20/09 — Sum-product estimates, Bourgain-Glibichuk-Koryagin theorem (part 1)

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Lecture 11/16/09 — Diophantine approximation (cont'd), Conclusion of Szemeredi for 4-term progressions

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• At end of lecture, list of possible topics for next semester

Lecture 11/13/09 — Local inverse theorem for U3, Diophantine approximation, Weyl's inequality

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Lecture 11/9/09 — U3 weak inverse (continued), U3 local inverse theorem,

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Lecture 11/6/09 — Gowers 4-term progression theorem, Generalized von Neumann for U3, weak inverse theorem for U3

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Lecture 11/2/09 — Balog-Szemeredi-Gowers, 4-term progressions and U3 norm, general U-norm properties

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Lecture 10/26/09 — Existence of highly 3-edge-connected subsets of dense bipartite graphs

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Lecture 10/23/09 — Chang's covering lemma, proof of Freiman-Rusza theorem, additive energy, Balog-Szemeredi-Gowers (easy direction)

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• Discussion on the rough classification problem of approximate groups
• Polynomial Freiman-Rusza conjecture

Lecture 10/21/09 — Minkowski 2nd Theorem (part 2), Bohr sets contain proper GAPs

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Lecture 10/7/09 — Rusza model lemma, Bogolyubov lemma, structure of Bohr sets, Minkowski 2nd theorem (part 1)

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Lecture 10/5/09 — (Structure of) Approximate groups and the Freiman-Rusza Theorem (for Z), Freimam morphisms, Rusza's model lemma

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Lecture 10/2/09 — Rusza's Third Inequality, (Structure of) Approximate groups and Rusza's Theorem (for F_2^\infty)

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• Ben Green's favorite open problem inside

Lecture 9/28/09 — Rusza calculus

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Lecture 9/25/09 — Inverse theorem for Gowers 2-norm, Dirichlet's Pigeons, end of Roth, Behrerd's example

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Lecture 9/21/09 — Progression-or-density theorem, Gowers 2-norm, Fourier on groups

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Lecture 9/18/09 — Overview, beginning of Roth

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