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

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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.