Conference: Arithmetic quantum field theory

算术量子场论会议将于2024年3月25日至29日在哈佛数学科学与应用中心(CMSA)举行。这将是一次面对面的聚会，约有70名研究人员--数学和物理专业的研究生、博士后和教职员工--以混合模式提供给不限数量的外部参与者。这次会议的一个中心焦点--也是第一天的专门目标--是鼓励女性在数学和物理领域的高水平参与。第一天旨在鼓励初级研究人员前来交流，在友好的环境中发表演讲，并参与其中，而不担心他们的研究是否准确地符合研讨会的狭隘主题。算术量子场论会议，以及为期两个月的同名项目，旨在通过传播在量子场论和代数数论之间，特别是在它们的基本不变量：配分函数和L函数之间出现的令人兴奋的新联系，来促进数学家和物理学家之间的相互作用。一方面，在过去的十年里，我们对量子场论背后的代数结构的理解有了巨大的进步，这些结构是用低维流形的几何和拓扑来表示的。另一方面，算术拓扑字典在流形的拓扑和数域的算法之间提供了一座牢固的桥梁。因此，人们现在可以将量子场论的想法转移到数论。该计划将汇集在相邻领域工作的广泛数学家和物理学家，探索新兴的算术量子场论概念，作为一种工具，将量子物理学应用于自同构形式理论、调和分析和L函数理论中感兴趣的问题，并反过来探索算术思想的潜在几何和物理后果。会议网站是https://cmsa.fas.harvard.edu/event/aqftconf/，会议的演讲录音和讲座笔记将广泛提供。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。

The conference Arithmetic Quantum Field Theory will be held at the Harvard Center of Mathematical Sciences and Applications (CMSA) on March 25-29 2024. This will be an in-person gathering of approximately 70 researchers - graduate students, postdocs, and faculty in mathematics and physics, available in hybrid mode to an unlimited number of outside participants. A central focus of the conference - and the dedicated aim of its first day - is to encourage a high level of participation by women in math and physics. The first day is designed to encourage junior researchers to come and network, give talks in a friendly environment, and participate without concern over the precise fit of their research to the narrow theme of the workshop. The conference Arithmetic Quantum Field Theory, and the two-month program of the same title it concludes, are aimed at catalyzing interactions between mathematicians and physicists by disseminating exciting new connections emerging between quantum field theory and algebraic number theory, and in particular between the fundamental invariants of each: partition functions and L-functions. On one hand, there has been tremendous progress in the past decade in our understanding of the algebraic structures underlying quantum field theory as expressed in terms of the geometry and topology of low-dimensional manifolds. On the other hand, the arithmetic topology dictionary provides a sturdy bridge between the topology of manifolds and the arithmetic of number fields. Thus, one can now port over quantum field theoretic ideas to number theory. The program will bring together a wide range of mathematicians and physicists working on adjacent areas to explore the emerging notion of arithmetic quantum field theory as a tool to bring quantum physics to bear on questions of interest for the theory of automorphic forms, harmonic analysis and L-functions, and conversely to explore potential geometric and physical consequences of arithmetic ideas.The conference website is https://cmsa.fas.harvard.edu/event/aqftconf/ where recordings of the talks and notes from lectures will be made widely available.This 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.