Conference: Additive Combinatorics 2024

该奖项支持美国研究生和博士后参加加法组合学2024，这是15年来加法组合学的第一次大型大会，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。本次大会将有五场由该领域资深专家进行的说明性全体演讲，十几场研究讲座和一场开放问题会议。加性组合数学仍然是一个高度活跃和充满活力的领域，与纯数学的其他分支有着许多深刻的联系和应用。自上一次加法组合学大会以来，该学科有了很大的发展。例如，近年来，我们看到了非交换群的近似子群的分类，在循环群和有限域上的向量空间的设置中Gowers一致范数的一个有效逆定理的证明，盖集问题中最佳上界的显著改进，Roth定理中近优界的证明，和积猜想的进一步发展，多项式Szemerédi定理中有效界的证明以及这些结果在点态遍历理论中的应用，高阶傅立叶分析在乘法函数相关关系中的应用，以及Sarnak关于Möbius函数对零熵流渐近正交性的猜想，关于张量的解析秩和分拆秩及有限域上向量空间中多项式Freiman-Ruzsa猜想的解的一系列工作。说明性全体讲座将概述加法组合学各个子领域的现状，研究讲座将涵盖最令人兴奋的最新突破。公开问题会议将为该领域的未来方向提供建议，对较初级的参与者尤其有用。会议网站：https://www.icms.org.uk/AdditiveCombinatoricsThis奖反映了美国国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.