Conference: Modular forms, L-functions, and Eigenvarieties

该奖项支持美国科学家参加“模形式、l函数和特征变种”会议。该活动将于2024年6月18日至21日在法国巴黎举行。整数是我们数学世界的原子。数论学家研究为什么模式会在整数中出现。在20世纪70年代，罗伯特·朗兰兹提出数论和数学对称性之间的联系。他的思想使这个领域发生了革命性的变化。一些最有成效的方法是通过几何空间的微积分来实现他的想法的。这里资助的会议将展示这些方法的前沿研究。会议上传播的思想将对这一领域产生广泛的影响。领军人物的演讲将推动初级研究人员研究新的理论。美国的与会者将对会议作出书面总结。这些摘要将鼓励下一代采用最新的观点。撰写它们还将在研究界产生一种合作精神。活动的摘要和细节将在网站https://www.eventcreate.com/e/bellaiche/上公布。会议的详细目的是在特征变的背景下揭示模形式和l函数的研究。特征变数是数论中编码同余现象的p进空间。本征型族、l函数族和其他算术对象在本征变体上找到它们的家。这次会议的主要目的是揭露这些家庭的最新研究成果。这些演讲将把新的研究及其应用放在一个地方，在p-adic Langlands项目的保护伞下。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，被认为值得支持。

This award supports US-based scientists to attend the conference "Modular Forms, L-functions, and Eigenvarieties". The event will take place in Paris, France from June 18, 2024, until June 21, 2024. Whole numbers are the atoms of our mathematical universe. Number theorists study why patterns arise among whole numbers. In the 1970's, Robert Langlands proposed connections between number theory and mathematical symmetry. His ideas revolutionized the field. Some of the most fruitful approaches to his ideas have come via calculus on geometric spaces. The conference funded here will expose cutting edge research on such approaches. The ideas disseminated at the conference will have a broad impact on the field. The presentations of leading figures will propel junior researchers toward new theories. The US-based participants will make a written summary of the conference. The summaries will encourage the next generation to adopt the newest perspectives. Writing them will also engender a spirit of collaboration within the research community. The summaries along with details of the events will be available on the website https://www.eventcreate.com/e/bellaiche/. The detailed aim of the conference is exposing research on modular forms and L-functions in the context of eigenvarieties. An eigenvariety is a p-adic space that encodes congruence phenomena in number theory. Families of eigenforms, L-functions, and other arithmetic objects find their homes on eigenvarieties. The conference's primary goal is exposing the latest research on such families. The presentations will place new research and its applications all together in one place, under the umbrella of the p-adic Langlands program.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.