CBMS Conference: Ramanujan's Partition Congruences, Mock Theta Functions, and Beyond

该奖项为作为数学科学会议委员会(CBMS)系列的一部分组织的“Ramanujan的队伍、模拟的theta函数及以后”研究会议提供资金。该活动将于2022年5月16日至20日在德克萨斯大学里奥格兰德山谷举行。这次活动的主要目的是向更广泛的受众介绍数学数论中的各种主题。会议将围绕佛罗里达大学盖恩斯维尔分校的弗兰克·加文教授所作的10场演讲展开。数学家斯里尼瓦萨·拉马努扬的发现已经在从超级计算到化学、物理和黑洞研究等学科中得到了应用。最近的工作是从创新使用数学理论和使用计算机代数系统获得的数据推动的。根据NSF-CBMS计划的目标，本次会议的主要目的是通过聚集对Q系列、模形式和划分感兴趣的领先数学家和初级研究人员来促进进一步的研究。我们预计，参加这次建立信任措施会议的许多科学家将来自墨西哥湾沿岸各州和墨西哥各地。这样的会议将对德克萨斯大学里奥格兰德山谷新的数学博士项目产生不可估量的影响。Garvan教授将讲授Ramanujan的分拆同余和模拟theta函数的主题。这些讲座和主题的观点可以追溯到物理学家弗里曼·戴森的工作。1944年，Dyson提出了Ramanujan著名的分拆同余的更深层次的组合原因。戴森的问题是加文在1987年完成的。戴森在他的文章《漫步拉马努扬的花园》中预见到，加尔万的美丽发现不是结束，而是开始。戴森提出了建立划分同余和模拟theta函数的宏大综合的挑战，以发展mock theta函数的群论结构。这种综合将类似于Hecke从雅可比的theta函数理论发展出的模形式，并将导致在物理学中的应用。加文教授将讲授现代数学如何应对戴森面临的这两个挑战。这将涉及组合技术和函数论方法，包括基本超几何函数的经典理论，以及现代的弱调和Maass形式和p-进模形式理论。有关会议的更多信息将在网站上获得：https://www.cbmsweb.orgThis奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award provides funding for the research conference "Ramanujan's ranks, mock theta functions, and beyond" organized as part of the Conference Board of the Mathematical Sciences (CBMS) series. The event will take place at University of Texas Rio Grande Valley during May 16-20, 2022. The main goal of this event is to provide an introduction to various topics in mathematical number theory to a broader audience. The conference revolves around ten lectures to be given by Professor Frank Garvan of the University of Florida Gainesville. The discoveries of the mathematician Srinivasa Ramanujan have found applications in disciplines from supercomputing to chemistry, and to physics and the study of black holes. Recent work has been motivated by data obtained from the innovative use of both mathematical theory and the use of computer algebra systems. In accordance with the goals of the NSF-CBMS program, the main purpose of this conference is to stimulate further research by bringing together leading mathematicians and junior researchers interested in q-series, modular forms, and partitions. We expect that many of the scientists attending this CBMS conference to come from all over the Gulf Coast States and Mexico. Such a conference will have immeasurable impact on the new doctoral program in mathematics that is planned at the University of Texas Rio Grande Valley. Professor Garvan will lecture on the topics of Ramanujan’s partition congruences and mock theta functions. The viewpoint of these lectures and topics goes back to the work of the physicist Freeman Dyson. In 1944 Dyson asked for deeper combinatorial reasons for Ramanujan's famous partition congruences. Dyson's question was completed by Garvan in 1987. In his article, A Walk through Ramanujan’s Garden, Dyson foresaw that "Garvan's beautiful discovery is not an end but a beginning." Dyson proffered the challenge to build a grand synthesis of partition congruences and mock theta functions to develop the group theoretic structure of mock theta functions. This synthesis would be analogous to Hecke's development of modular forms from Jacobi's theory of theta functions and would lead to applications in physics. Professor Garvan will lecture on how modern mathematics has taken up both of Dyson's challenges. This will involve combinatorial techniques and function theoretic methods including the classical theory of basic hypergeometric functions as well the modern theory of weak harmonic Maass forms and p-adic modular forms. Further information about the conference will be available at the website: https://www.cbmsweb.orgThis 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.