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研究会议“拉马努金的行列，模拟θ函数及其他”提供资金。该活动将于2022年5月16日至20日在德克萨斯大学格兰德河谷举行。该活动的主要目标是向更广泛的受众介绍数学数论中的各种主题。会议围绕着佛罗里达盖恩斯维尔大学的弗兰克·加文教授的十个讲座展开。数学家Srinivasa Ramanujan的发现已经在从超级计算到化学，物理学和黑洞研究的学科中找到了应用。 最近的工作一直受到数学理论和计算机代数系统的创新使用所获得的数据的激励。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系列，模形式和分区感兴趣的领先数学家和初级研究人员来刺激进一步的研究。 我们希望参加这次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河谷分校计划的新的数学博士课程产生不可估量的影响。 Garvan教授将讲授Ramanujan的分区同余和模拟θ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。戴森在1944年要求更深层次的组合原因拉马努金的著名分区同余。 戴森的问题由Garvan在1987年完成。在他的文章《漫步拉马努金花园》中，戴森预见到“加文的美丽发现不是结束，而是开始。“戴森提出了挑战，要建立分区全等和模拟theta函数的大合成，以开发模拟theta函数的群论结构。这种综合将类似于赫克的发展模块形式从雅可比理论的θ函数，并将导致应用在物理学。Garvan教授将讲述现代数学如何应对戴森的挑战。 这将涉及组合技术和函数理论方法，包括基本超几何函数的经典理论以及弱调和马斯形式和p-adic模形式的现代理论。有关会议的进一步信息将在网站上提供：https://www.cbmsweb.orgThis奖项反映了NSF的法定使命，并被认为值得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来支持。

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.