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Alice Guionnet, Assaf Naor, Gilles Pisier, Sorin Popa, Dimitri Shylakhtenko, and I are organising a three month program here at the Institute for Pure and Applied Mathematics (IPAM) on the topic of Quantitative Linear Algebra. The purpose of this program is to bring together mathematicians and computer scientists (both junior and senior) working in various quantitative aspects of linear operators, particularly in large finite dimension. Such aspects include, but are not restricted to discrepancy theory, spectral graph theory, random matrices, geometric group theory, ergodic theory, von Neumann algebras, as well as specific research directions such as the Kadison-Singer problem, the Connes embedding conjecture and the Grothendieck inequality. There will be several workshops and tutorials during the program (for instance I will be giving a series of introductory lectures on random matrix theory).

While we already have several confirmed participants, we are still accepting applications for this program until Dec 4; details of the application process may be found at this page.

The Institute for Pure and Applied Mathematics (IPAM) here at UCLA is seeking applications for its new director in 2017 or 2018, to replace Russ Caflisch, who is nearing the end of his five-year term as IPAM director. The previous directors of IPAM (Tony Chan, Mark Green, and Russ Caflisch) were also from the mathematics department here at UCLA, but the position is open to all qualified applicants with extensive scientific and administrative experience in mathematics, computer science, or statistics. Applications will be reviewed on June 1, 2016 (though the applications process will remain open through to Dec 1, 2016).

This is an adaptation of a talk I gave recently for a program at IPAM. In this talk, I gave a (very informal and non-rigorous) overview of Hrushovski’s use of model-theoretic techniques to establish new Freiman-type theorems in non-commutative groups, and some recent work in progress of Ben Green, Tom Sanders and myself to establish combinatorial proofs of some of Hrushovski’s results.

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