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.

该奖项支持美国科学家参加“模形式、L函数和特征变量”会议。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。数论学家研究的是为什么模式会出现在整数中。在1970年代，罗伯特·朗兰兹提出了数论和数学对称性之间的联系。他的思想彻底改变了这个领域。一些最富有成效的方法来他的想法已经通过微积分的几何空间。这里资助的会议将揭示关于这种方法的前沿研究。会议上传播的思想将对该领域产生广泛影响。领军人物的演讲将推动初级研究人员走向新理论。美国的与会者将对会议进行书面总结。这些摘要将鼓励下一代采用最新的观点。撰写这些报告还将在研究界产生一种合作精神。这些活动的摘要沿着以及详细情况将在网站https://www.eventcreate.com/e/bellaiche/上公布。会议的详细目的是在特征变量的背景下揭示模形式和L-函数的研究。本征簇是一个p进空间，它编码了数论中的同余现象。本征形、L-函数和其他算术对象的族在本征簇上找到了它们的家。这次会议的主要目的是揭露关于这类家庭的最新研究。该奖项反映了NSF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。