This funding is for the conference "Representation Theory, Automorphic Forms, and Complex Geometry" to be held at Harvard University from May 20th to 23rd, 2013. There will be approximately 16 speakers and an anticipated 100 participants. The conference will have two major themes. The first consists of recent approaches to understanding the unitary dual of a semisimple Lie group, a fundamental problem in both representation theory and automorphic forms. Several of the talks will describe recent advances in computing the unitary dual, understanding unitarity through Hodge structures, and constructing unitary representations using global methods (for example, via Arthur's conjectures on the discrete spectrum). The second theme is the application of geometric constructions in representation theory to problems in automorphic forms, in particular to analytic number theory and the study of L-functions. We hope that bringing together experts in these various branches of mathematics will encourage collaborations in new directions.

By its very nature, the conference seeks to connect different areas of mathematical research, and thus should be useful in exposing researchers of all levels to ideas which have increasing importance. The grant includes funding for graduate student participation, in particular, and also funding for postdocs, young researchers, and mathematicians from underrepresented groups. We hope that the conference will draw not only mathematicians who work directly in these two areas, but also others from neighboring areas of mathematics and mathematical physics. The conference website can be found at

Project Report

on May 20-23, 2013. There were talks from leaders in all three fields, and list of open problems was compiled. Some of the speakers included: Benedict Gross (Harvard University), David Kazhdan (Hebrew University), Dennis Gaitsgory (Harvard University), Jim Arthur (University of Toronto), Kari Vilonen (Northwestern University), David Vogan (MIT), Nolan Wallach (UCSD), Peter Sarnak (Princeton University), Carlos Simpson (Toulouse University), Alina Marian (Northeastern University), Diana Shelstad (Rutgers University) and Joseph Harris (Harvard University). Some of the central topics covered were an examination of the unitary dual of real reductive groups, functorality for automorphic forms, variation of Hodge structures and non-abelain Hodge theory, and the applications of representation theory to questions in analytic number theory. The session on open problems was led by Barry Mazur and generated a host of new questions for the next generation. In particular, the conference was well attended by students - there were over two hundred people attending the lectures. Information on the attendees, open problems, titles and abstracts of all the talks can be found on the following website: The conference was a great success in communicating the main ideas in the subject to a wide audience.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
Standard Grant (Standard)
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Program Officer
Eric Sommers
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Harvard University
United States
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