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“国际功能和自动形态国际会议”的会议提供了支持，该会议将于5月13日至16日在田纳西州纳什维尔的范德比尔特大学2024年在田纳西州纳什维尔大学举行。这是范德比尔特（Vanderbilt）举办的年度系列的一部分。在数字理论上拥有悠久的历史，并且在这些领域建立和进一步的对话，这是一个非常活跃的研究领域。 Riemann假设的扩展适用于与自动形式相关的L功能。尽管已经制定了许多围绕L功能的概括和应用，但它们中仍然存在各种基本的开放问题，包括限制和L-功能的价值分布。前者与追求L功能的所谓亚凸度范围有关。后者与桦木和Swinnterton-Dyer猜想有关（克莱数学研究所提出的另一个“千年问题”）。这些追求与Langlands计划密切相关，Langlands计划是一种与自动形式相关的“统一理论”。可以在会议网站https://my.vanderbilt.edu/shanksseries/.This奖上找到更多详细信息，这反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响审查标准，被认为是通过评估来获得的支持。