Conference: Additive Combinatorics 2024

该奖项支持美国的研究生和博士后参加Additive Combinatorics 2024，这是15年来第一次重大的加法组合学大会，将于2024年7月22日至2024年7月26日在苏格兰爱丁堡的ICMS举行。本次会议将包括五个由该领域资深专家组成的临时全体会议，十几个研究讲座和一个开放问题会议。加性组合学仍然是一个高度活跃和动态的领域，与纯数学的其他分支有许多深刻的联系和应用。自从上一次加性组合学大会以来，这门学科有了巨大的发展。例如，近年来我们看到了非交换群的近似子群的分类，证明了有限域上循环群和向量空间的Gowers一致性范数的有效逆定理，帽集问题中最佳上界的显着改进，Roth定理中近最优界的证明，和积猜想的进一步进展，证明多项式Szemerédi定理的有效界沿着与应用这些结果逐点遍历理论，应用高阶傅立叶分析的相关性的乘法函数和Sarnak的猜想的渐近正交性的莫比乌斯函数零熵流，一系列的作品有关的分析和分区秩张量，以及多项式Freiman-Ruzsa猜想在有限域上向量空间中的归结。临时全体讲座将调查加法组合学的各个子领域的现状，研究讲座将涵盖最令人兴奋的最新突破。开放性问题会议将建议该领域未来的方向，并应特别为初级participator.Conference网站：https://www.icms.org.uk/AdditiveCombinatoricsThis奖反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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/AdditiveCombinatoricsThis 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.