Conference on "100 Years of Mock Theta Functions; New Directions in Partitions, Modular Forms, and Mock Modular Forms"

该奖项为“模拟Theta函数的100年：分区、模块形式和模拟模块形式的新方向”会议提供了部分支持。本次会议恰逢拉马努金在致哈代的临终信中提出最初定义100周年，将于2020年5月18日至19日在田纳西州纳什维尔的范德比尔特大学举行。主题将是围绕分区领域的新发展，特别是等级、曲柄和其他分区统计。这次会议的目的是建立和促进关于组合学和模块形式边界的新发展的对话。这将促进在这些领域工作的研究人员之间的合作，会议将有一个问题会议来描述和传播关键问题，以及一个关于影响初级和少数民族研究人员的问题的讨论小组。特别是，模形式和模拟模形式一直是研究分区和其他组合序列的重要工具。模拟函数在秩和曲柄同余、渐近性和不等式上得到了许多结果，相反，这种划分统计推动了调和质量形式的发展。最近，斯坦顿在未发表的笔记中强调了他和加文的几个猜想。这些猜想寻求秩和曲柄统计的组合精化。这表明在组合方面和模拟模块形式世界中都有更深层次的结构。这些猜想有可能在组合学和模拟函数的交叉领域开辟新的研究领域。考虑到这些前沿问题和Ramanujan引入模拟theta函数周年纪念日的合适性质，这是一个特别合适的时机，聚集来自这两个领域的专家来讨论这些问题和相关主题的未来，并让下一代初级研究人员参与这次对话和合作。更多的细节可以在会议网站上找到：https://my.vanderbilt.edu/mock/This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。

This award provides partial support for the conference "100 Years of Mock Theta Functions: New Directions in Partitions, Modular Forms, and Mock Modular Forms." This conference falls on the 100 year anniversary of Ramanujan's original definition in his deathbed letter to Hardy and will take place at Vanderbilt University in Nashville, Tennessee on May 18-19 2020. The main theme will be on new developments around the area of partitions, and especially ranks, cranks, and other partition statistics. This conference is oriented at establishing and furthering dialogue on new developments at the boundary of combinatorics and modular forms. This will foster collaboration between researchers working in these fields, and the conference will feature a problem session to delineate and disseminate critical questions, as well as a discussion panel about issues affecting junior and minority researchers. In particular, modular forms and mock modular forms have long been essential tools in the study partitions and other combinatorial sequences. Mock theta functions have led to many results on rank and crank congruences, asymptotics, and inequalities, and conversely, such partition statistics have motivated the development of harmonic Maass forms. Very recently, Stanton has highlighted several conjectures of his and Garvan's in unpublished notes. These conjectures seek a combinatorial refinement of the rank and crank statistics. These suggest a deeper structure both on the combinatorial side and in the mock modular form world. These conjectures have the potential to open up new areas of research at the intersection of combinatorics and mock theta functions. Given these cutting-edge questions and the fitting nature of Ramanujan's anniversary of introducing mock theta functions, it is a particularly opportune time to gather experts from these two fields to discuss the future of such questions and related topics, and to involve the next generation of junior researchers in this conversation and collaboration. Further details can be found on the conference website: https://my.vanderbilt.edu/mock/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.