Mock theta functions and applications in combinatorics, algebraic geometry, and mathematical physics

该补助金支持会议``模拟θ函数和应用组合，代数几何和数学物理”，这将发生在2009年5月25日至29日，在马克斯普朗克数学研究所在波恩（德国）。 赠款资金将用于使美国的研究人员能够参加这次国际会议。 会议将推进模拟θ函数的理论和应用，汇集世界一流的研究人员，不仅在模拟θ函数本身，而且在影响这个非常活跃的领域的不同领域。 模拟θ函数最近成为数学研究中一个特别活跃的领域。 这些功能介绍了拉马努金在他的最后一封信哈代于1920年，但很长一段时间，鲜为人知的是，这些职能。 在2002年，茨韦格的博士论文提供了一个重要的联系之间的模拟theta函数和谐波马斯形式。 这一课题的突破为丰富的研究领域打开了大门。 从那时起，模拟theta函数在物理学中的各种数学领域和主题的应用导致了重大开放问题的解决方案。 尽管它最近发展迅速，但仍有许多开放的问题和进一步的应用（在数学和物理的不同领域）需要调查。会议不仅将促进我们对模拟theta函数的理解，而且还为与会者提供了一个重要而及时的机会，开始新的合作，并加强现有的合作。 高级研究人员之间的国际联系间接地使学生和博士后受益，他们以后可能会访问国外的机构进行演讲，学习或担任访问职位。 初级参与者将能够在其职业生涯的关键阶段与国际专家一起开始新项目。

This grant supports the conference ``Mock theta functions and applications in combinatorics, algebraic geometry, and mathematical physics", which will take place May 25--29, 2009, at the Max Planck Institute for Mathematics in Bonn (Germany). Grant funds will be used to enable US-based researchers to participate in this international meeting. The meeting will advance the theory and applications of mock theta functions by bringing together world class researchers with expertise not only in mock theta functions themselves, but also in the diverse areas that impact this very active field. Mock theta functions have recently become a particularly active area of research in mathematics. These functions were introduced by Ramanujan in his last letter to Hardy in 1920, but for a long time, little was known about these functions. In 2002, Zweger's PhD thesis provided an important link between mock theta functions and harmonic Maass forms. This breakthrough in the subject opened the door to a rich area of research. Since then, applications of mock theta functions to various mathematical fields and topics in physics have led to solutions of major open problems. Despite its recent rapid development, there are still many open problems and further applications (in different areas of mathematics and physics) needing investigation.The conference will not only advance our understanding of mock theta functions, but also provide an important and timely opportunity for participants to start new collaborations and strengthen existing collaborations. International connections between senior researchers indirectly benefit students and post-docs, who may later visit institutions abroad to give talks, study, or hold visiting positions. Junior participants will be able to start new projects with international experts at a critical stage in their careers.