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

该奖项为会议“100年模拟Theta函数：分区，模块化形式和模拟模块化形式的新方向”提供部分支持。“这次会议福尔斯落在拉马努金在他的临终前给哈代的信中的原始定义的100周年纪念日，并将于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。主题将围绕分区的新发展，特别是等级，曲柄和其他分区统计。本次会议的目的是建立和深化关于组合学和模块化形式边界新发展的对话。这将促进在这些领域工作的研究人员之间的合作，会议将以一个问题会议为特色，以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长期以来一直是研究分区和其他组合序列的重要工具。 模拟θ函数导致了许多结果的秩和曲柄同余，渐近性和不平等，相反，这种分区统计的发展，促进了谐波马斯形式。 最近，斯坦顿在未发表的笔记中强调了他和加文的几个观点。 这些结构寻求一个组合细化的排名和曲柄统计。这些都暗示了在组合方面和在模拟模形式世界中的更深层次的结构。这些结构有可能在组合学和模拟theta函数的交叉点上开辟新的研究领域。考虑到这些前沿问题和拉马努金引入模拟θ函数周年纪念日的合适性质，这是一个特别合适的时机，可以聚集这两个领域的专家来讨论这些问题和相关主题的未来，并让下一代的初级研究人员参与这种对话和合作。更多细节可在会议网站上找到：https://my.vanderbilt.edu/mock/This奖项反映了NSF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，被认为值得支持。

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 Very recently, Stanton has highlighted several conjectures of his and Garvan's in unpublished notes.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.