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.

该奖项为名为“l函数和自同构形式国际会议”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。这是由范德比尔特大学主办的年度系列会议的一部分，被称为香克斯系列会议。主题将是标题所示领域之间的新发展和最近的相互作用。自同构形式和l函数之间的相互作用在数论中有着悠久而富有成果的历史，连接这两个领域仍然是一个非常活跃的研究领域。这次会议的目的是就这些地区边界的新发展建立和促进对话。这将促进在这些领域工作的研究者之间的合作。现代数论的一个美丽特征是，如果黎曼假设的自然扩展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等不同研究领域中，许多广泛感兴趣的问题都可以以本质上最优的方式解决。虽然关于l -函数的许多推广和应用已经得到了解决，但其中仍有许多基本的开放性问题需要解决，包括l -函数的界和值分布。前者与追求所谓的l函数的次凸界有关。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。这些追求与朗兰兹纲领密切相关，朗兰兹纲领是一个关于自同构形式的“大统一理论”。更多的细节可以在会议网站https://my.vanderbilt.edu/shanksseries/.This上找到，该奖项反映了美国国家科学基金会的法定使命，并通过基金会的智力价值和更广泛的影响审查标准进行评估，认为值得支持。