Conference: Additive Combinatorics 2024

This award supports participation of US-based graduate students and postdocs in Additive Combinatorics 2024, the first major general conference in additive combinatorics in 15 years, which will be held 7/22/2024-7/26/2024 at the ICMS in Edinburgh, Scotland. This conference will feature five expository plenary talks by senior experts in the field, around a dozen research talks, and an open problem session. Additive combinatorics continues to be a highly active and dynamic field, and has many deep connections and applications to other branches of pure mathematics. Since the last major general conference in additive combinatorics, the subject has developed enormously. For example, in recent years we have seen the classification of approximate subgroups of nonabelian groups, proofs of an effective inverse theorems for the Gowers uniformity norms in both the setting of cyclic groups and of vector spaces over finite fields, a dramatic improvement in the best upper bounds in the cap set problem, a proof of near-optimal bounds in Roth's theorem, further progress on the sum-product conjecture, proofs of effective bounds in the polynomial Szemerédi theorem along with applications of these results to pointwise ergodic theory, applications of higher-order Fourier analysis to correlations of multiplicative functions and Sarnak's conjecture on the asymptotic orthogonality of the Möbius function to zero entropy flows, a series of works relating the analytic and partition rank of tensors, and the resolution of the polynomial Freiman--Ruzsa conjecture in vector spaces over finite fields. The expository plenary lectures will survey the current state of various subfields of additive combinatorics, and the research lectures will cover the most exciting recent breakthroughs. The open problem session will suggest future directions for the field, and should be particularly useful for the more junior participants. Conference website: https://www.icms.org.uk/AdditiveCombinatorics This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.