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年来第一次主要的加法组合大会，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。本次会议将包括五场由该领域资深专家进行的说明性全体会议，大约十几个研究会议和一个公开问题会议。加性组合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。自上一届加性组合学大会以来，这门学科得到了巨大的发展。例如，近年来我们看到了非abel群的近似子群的分类，证明了循环群和有限域上向量空间的Gowers一致范数的有效逆定理，极大地改进了帽集问题的最佳上界，证明了Roth定理的近最优界，在和积猜想上取得了进一步的进展，多项式szemerdi定理的有效界的证明以及这些结果在点遍历理论中的应用，高阶傅立叶分析在乘法函数的相关性中的应用，以及Sarnak关于Möbius函数对零熵流的渐近正交性的猜想，一系列关于张量的解析秩和分配秩的工作，以及有限域上向量空间中多项式Freiman—Ruzsa猜想的解析。说明性全体讲座将调查加性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。开放问题会议将建议该领域的未来方向，并且应该对更初级的参与者特别有用。该奖项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知识价值和更广泛的影响审查标准进行评估，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.