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

该基金支持“模拟θ函数及其在组合学、代数几何和数学物理中的应用”会议，该会议将于2009年5月25日至29日在德国波恩的马克斯普朗克数学研究所举行。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。会议将通过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的专业知识，来推进模拟θ函数的理论和应用。模拟函数最近成为数学中一个特别活跃的研究领域。这些函数是拉马努金在1920年给哈代的最后一封信中介绍的，但很长一段时间以来，人们对这些函数知之甚少。2002年，Zweger的博士论文提供了模拟θ函数与谐波质量形式之间的重要联系。这一学科上的突破为丰富的研究领域打开了大门。从那时起，模拟theta函数在各种数学领域和物理主题中的应用导致了重大开放问题的解决方案。尽管近年来发展迅速，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）需要研究。这次会议不仅将促进我们对模拟theta函数的理解，而且为参与者提供了开始新的合作和加强现有合作的重要和及时的机会。高级研究人员之间的国际联系间接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启动新项目。

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.