This award will support an NSF/CMBS regional conference to be held at Texas Christian University in the summer of 2012 on the topic of Hodge theory, complex geometry, and representation theory. The principal speaker will be Professor Emeritus Phillip Griffiths from the Institute for Advanced Study. This award will support 30 participants at different stages of their careers.
This conference will describe recent progress on automorphic cohomology beyond the classical cases. The material involved is at the confluence of several parts of mathematics: Hodge theory, representation theory, and complex geometry. The main lectures will describe new breakthroughs due to Carayol and others and will build upon the recent work of Griffiths and his collaborators on Mumford-Tate groups and domains. The lectures will focus on two main examples and are intended to be accessible to a wide range of participants.
," that was held June 18-22, 2012, on the campus of Texas Christian University in Fort Worth, Texas. The main purpose of this CBMS conference was to bring together an outstanding collection of mathematicians to discuss some of the latest and most exciting questions that presently exist at the confluence of the mathematic fields represented in the title, in particular recent breakthroughs due to H. Carayol and others leading to recent work of Phillip Griffiths and his collaborators on Mumford-Tate groups and domains. This is an active and engaging field of mathematics with widespread applications. The 39 participants at the conference came from a wide geographical area, including not just the United States, but also two participants from each of Mexico, Canada, and France, and one each from Argentina, Japan, and Taipei. The participants also represented a broad degree of backgrounds, ranging from beginning graduate students to highly recognized and internationally known experts. This NSF grant included funds to provide travel support, lodging, and other accommodations for many of the conference participants, including graduate students and junior faculty who would not otherwise have possessed the means to attend. The principal speaker was Emeritus Professor Phillip Griffiths of the Institute for Advanced Study. Professor Griffiths delivered ten lectures (two a day for each of the five days) on the topics described in the title of the conference (abstracts of his lectures are given at the web site http://faculty.tcu.edu/gfriedman/CBMS2012/abstracts.html). Throughout the week Prof. Griffiths made an effort to carefully communicate with those who may not be experts in the topics being discussed and provided a full set of lecture notes for participants to follow. These notes can be found on the main conference page at http://faculty.tcu.edu/gfriedman/CBMS2012/ . Early in the week, the conference also featured background talks by Prof. Griffiths's close collaborators Mark Green and Matt Kerr. Another nine supplementary lectures were provided by expert participants, who worked hard to keep their talks accessible to the broad audience. Specific mathematical topics included transcendence degree of the field of periods, asymptotics of the period map, algebraicity of automorphic representations, real and complex compact and cemisimple Lie groups and finite dimensional representation theory, representations of SL_2, Hodge type conjectures and the Bloch-Kato Theorem, boundary components of Mumford-Tate domains, Schubert integrals and invariant characteristic cohomology of the infinitesimal period relation, period domains and Kahler manifolds, and log mixed Hodge theory. Additionally, there were two question sessions during which all participants were invited to ask questions of Prof. Griffiths or the other speakers. Prof. Griffiths's lectures will for the foundation for a book to be published by the CBMS in conjunction with the American Mathematical Society (AMS), while a separate proceedings volume, also to be published by the AMS, is anticipated and in process. The conference web site at http://faculty.tcu.edu/gfriedman/CBMS2012 contains abstracts of all the talks, as well as slides of some of these talks, a full schedule, a list of participants, registration procedures, and a description of housing arrangements. Breakfasts, lunches, and coffee breaks were catered throughout the five days, and at night participants went to various well-known restaurants. A welcoming reception was provided on the eve of the conference. Participants made it clear, via many comments and statements of thanks, how much they appreciated the efforts made by the organizers to meet their needs during the week. By all accounts the conference was a resounding success, thanks to the generosity of the National Science Foundation and the Conference Board of the Mathematical Sciences whose funds and infrastructure made the conference possible.
