Conference: Algebraic Cycles, Motives and Regulators

该奖项是为了支持美国参与监管机构V，这是一系列致力于监管机构理论数学的国际会议中的第五次，将于2024年6月3日至13日在比萨大学举行。调节器会议是一个国际公认的和备受尊敬的系列会议，主题围绕调节器理论，其中许多在最近的数学突破中发挥了关键作用。会议将汇集来自不同职业阶段的多元化参与者，从研究生到高级教授，并为演讲，交流思想和开始新的合作提供支持性环境。传统上，对于这些领域的早期职业研究人员来说，这是一个富有成效的地方，可以与其他机构的潜在合作者和导师联系，研究相关主题。这个奖项主要是为了支持这些参与者。调节器在代数几何和数论中发挥着核心作用，是将代数循环和动机与数论和算术联系起来的共同线索。他们是中心的对象出现在几个著名的apturtures有关的L-职能和代数周期，包括伯奇-斯温纳顿戴尔猜想，和apturtures德利涅，贝林森，和布洛赫-加藤有关特殊价值的L-职能的品种代数周期和K-理论。这些对象的研究导致了相关领域的发展，包括岩泽理论，K理论和动机同伦理论。它们也出现在代数几何和数论之外的许多数学领域，最显著的是数学物理。Regulators V的主题可能包括Iwasawa理论和p-adic L-函数，K-理论，motivic同伦理论，动机和代数循环，霍奇理论，特征p的微局部分析，L-函数的特殊值以及其他相关研究领域的最新发展，包括数学物理应用http://regulators-v.dm.unipi.it/regulators-v-web.htmlThis。基金会的使命是履行其法定使命，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，被认为值得支持。

This award is to support US participation in Regulators V, the fifth in a series of international conferences dedicated to the mathematics around the theory of regulators, that will take place June 3-13, 2024, at the University of Pisa. The Regulators conferences are an internationally recognized and well-respected series of conferences on topics surrounding the theory of Regulators, many of which have played a key role in recent breakthroughs in mathematics. The conference will bring together a diverse group of participants at a wide range of career stages, from graduate students to senior professors and provide a supportive environment for giving talks, exchanging ideas, and beginning new collaborations. This has traditionally been a fruitful place for early career researchers in these fields to connect with potential collaborators and mentors at other institutions, working on related topics. This award is mainly to support such participants.Regulators play a central role in algebraic geometry and number theory, being the common thread relating algebraic cycles and motives to number theory and arithmetic. They are the central objects appearing in several well-known conjectures relating L-functions and algebraic cycles, including the Birch--Swinnerton-Dyer conjecture, and conjectures of Deligne, Beilinson, and Bloch-Kato relating special values of L-functions of varieties to algebraic cycles and K-theory. The study of these objects have led to the development of related fields including Iwasawa theory, K-theory, and motivic homotopy theory. They also appear in many areas of mathematics outside algebraic geometry and number theory, most notably in mathematical physics. The topics covered at Regulators V are likely to include recent developments in Iwasawa theory and p-adic L-functions, K-theory, motivic homotopy theory, motives and algebraic cycles, hodge theory, microlocal analysis in characteristic p, and special values of L-functions and additional related areas of research including applications to mathematical physics.Additional information can be found on the conference website: http://regulators-v.dm.unipi.it/regulators-v-web.htmlThis 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.