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

该奖项为“拉马努金的秩，模拟θ函数及其他”研究会议提供资金，该会议是数学科学会议委员会（CBMS）系列会议的一部分。该活动将于2022年5月16日至20日在德克萨斯大学格兰德谷分校举行。这次活动的主要目标是向更广泛的受众介绍数学数论的各种主题。会议将由佛罗里达大学盖恩斯维尔分校的弗兰克·加文教授进行10场讲座。数学家斯里尼瓦萨·拉马努金的发现在超级计算、化学、物理学和黑洞研究等学科中得到了应用。最近的工作是由从数学理论和计算机代数系统的创新使用中获得的数据所激励的。根据NSF-CBMS计划的目标，本次会议的主要目的是通过汇集对q级数、模形式和分区感兴趣的顶尖数学家和初级研究人员来促进进一步的研究。我们期待参加这次CBMS会议的许多科学家来自墨西哥湾沿岸各州和墨西哥。这样的会议将对德克萨斯大学格兰德谷分校计划开设的新的数学博士课程产生不可估量的影响。加文教授将会讲拉马努金的配分同余和模拟函数。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，戴森为拉马努金著名的分割同余寻找更深层次的组合原因。戴森的问题在1987年由加文完成。在他的文章《漫步拉马努金的花园》中，戴森预见到“加文的美丽发现不是结束，而是开始。”Dyson提出了建立配分同余和模拟函数的大综合的挑战，以发展模拟函数的群论结构。这种综合将类似于赫克从雅可比函数理论中发展出的模形式，并将在物理学中得到应用。加文教授将讲授现代数学如何应对戴森的这两个挑战。这将涉及组合技术和函数理论方法，包括经典的基本超几何函数理论以及现代的弱调和质量形式和p进模形式理论。有关会议的更多信息可在网站上获得：https://www.cbmsweb.orgThis该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知识价值和更广泛的影响审查标准进行评估，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.