Conference: Algebraic Cycles, Motives and Regulators

该奖项旨在支持美国参与监管机构V，这是致力于围绕监管机构理论的数学问题的一系列国际会议的第五次，该会议将于2024年6月3日至13日在比萨大学举行。监管机构会议是国际公认的、备受尊敬的一系列会议，主题围绕监管机构理论，其中许多会议在最近的数学突破中发挥了关键作用。会议将汇聚不同职业阶段的参与者，从研究生到高级教授，并为演讲、交流想法和开始新的合作提供一个支持性的环境。对于这些领域的早期职业研究人员来说，这传统上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，从事相关主题的工作。这一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。它们是几个著名的关于L函数和代数环的猜想的中心对象，包括Birch-Swinnerton-Dyer猜想，Deligne，Beilinson和Bloch-Kato将簇的L-函数的特殊值与代数圈和K-理论联系起来的猜想。对这些对象的研究导致了相关领域的发展，包括岩泽理论、K-理论和理据同伦理论。它们还出现在代数几何和数论之外的许多数学领域，最突出的是在数学物理中。会议主题可能包括岩泽理论和p-进L函数、K理论、动机同伦理论、动机和代数循环、霍奇理论、特征p中的微局部分析、L函数的特殊价值和其他相关研究领域(包括在数学物理中的应用)的最新发展。其他信息可在会议网站上找到：http://regulators-v.dm.unipi.it/regulators-v-web.htmlThis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.