Conference: International Conference on L-functions and Automorphic Forms

会议：L-函数和自同构国际会议

• 批准号: 2349888
• 负责人: Larry Rolen
• 金额: $ 2.5万
• 依托单位: Vanderbilt University
• 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 2025-03-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2349888&HistoricalAwards=false
• 关键词: Conference; International; functions; Automorphic; Forms

This award provides support for the conference entitled "International Conference on L-functions and Automorphic Forms'', which will take place at Vanderbilt University in Nashville, Tennessee on May 13--16 2024. This is part of an annual series hosted by Vanderbilt, known as the Shanks conference series. The main theme will be on new developments and recent interactions between the areas indicated in the title. The interplay between automorphic forms and L-functions has a long and very fruitful history in number theory, and bridging both fields is still a very active area of research. This conference is oriented at establishing and furthering dialogue on new developments at the boundary of these areas. This will foster collaboration between researchers working in these fields. One beautiful feature of modern number theory is that many problems of broad interest, in areas of study as diverse as arithmetic geometry to mathematical physics, can be solved in an essentially optimal way if the natural extension of the Riemann hypothesis holds for L-functions associated to automorphic representations. Although many generalizations and applications around L-functions have have already been worked out, there are still various fundamental open problems among them to tackle, including bounds for and the value distribution of L-functions. The former is related to the pursuit of so-called sub-convexity bounds for L-functions. The latter is related to the Birch and Swinnterton-Dyer conjecture (another “Millenium problem” posed by the Clay Mathematics institute). These pursuits are closely connected with the Langlands program, a “grand unifying theory” relating automorphic forms. Further details can be found on the conference website https://my.vanderbilt.edu/shanksseries/.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.

该奖项为题为“L 函数和自同构国际会议”的会议提供支持，该会议将于 2024 年 5 月 13 日至 16 日在田纳西州纳什维尔的范德比尔特大学举行。这是范德比尔特主办的年度系列会议的一部分，称为 Shanks 会议系列，主题将是标题中所示的领域之间的新发展和最近的相互作用。自守形式和 L 函数之间的相互作用有着悠久而富有成果的历史。理论，并且弥合这两个领域仍然是一个非常活跃的研究领域，本次会议旨在建立和促进这些领域边界的新发展对话，这将促进这些领域的研究人员之间的合作。现代数论的一个重要特征是，如果黎曼假设的自然外延适用于与自同构表示相关的 L 函数，那么在从算术几何到数学物理学等不同研究领域中，许多引起广泛关注的问题都可以以本质上最优的方式解决许多概括和围绕L函数的应用已经被研究出来，其中仍然存在各种基本的开放问题需要解决，包括L函数的界限和值分布，前者与追求所谓的次凸性有关。后者与 Birch 和 Swinnterton-Dyer 猜想（克莱数学研究所提出的另一个“千年问题”）有关。有关自同构形式的“大统一理论”的更多详细信息可以在会议网站 https://my.vanderbilt.edu/shankseries/ 上找到。该奖项反映了 NSF 的法定使命，并通过使用基金会的知识进行评估，认为值得支持。优点和更广泛的影响审查标准。