Conference: Modular forms, L-functions, and Eigenvarieties

会议：模形式、L 函数和特征变量

• 批准号: 2401152
• 负责人: John Bergdall
• 金额: $ 1.5万
• 依托单位: University of Arkansas
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-04-01 至 2024-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2401152&HistoricalAwards=false
• 关键词: Conference; Modular; forms; functions; Eigenvarieties

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.

该奖项支持美国的科学家参加会议“模块化形式，l功能和特征值”。该活动将于2024年6月18日至2024年6月21日在法国巴黎举行。整数是我们数学宇宙的原子。数字理论家研究为什么模式在整数中会出现。在1970年代，罗伯特·兰兰兹（Robert Langlands）提出了数字理论与数学对称性之间的联系。他的想法彻底改变了领域。一些最富有成果的方法是通过微积分在几何空间上进行的。这里资助的会议将使有关此类方法的最先进研究。会议上传播的想法将对该领域产生广泛的影响。领先人物的演讲将使初级研究人员转向新理论。美国的参与者将进行书面摘要。摘要将鼓励下一代采用最新的观点。编写它们还将在研究社区内部具有协作精神。这些摘要以及活动的详细信息将在网站https://www.eventcreate.com/e/bellaiche/上找到。该会议的详细目的是在特征值下对模块化形式和L功能进行研究。特征变量是一个编码数字理论一致性现象的P-ADIC空间。特征形式，l功能和其他算术对象的家族在特征值上找到了家园。会议的主要目标是揭露有关此类家庭的最新研究。演讲将在P-Adic Langlands计划的保护下将新的研究及其应用程序融合在一起。该奖项反映了NSF的法定任务，并被认为是通过基金会的知识分子和更广泛的影响评估标准的评估来通过评估来支持的。