The conference "Automorphic forms, representations, and combinatorics" will take place at Stanford University from August 13--16, 2012, and highlight recent research by Daniel Bump and his many collaborators and students. Their results connect various matrix coefficients to the geometry and combinatorics of a certain class of singular algebraic varieties. Many of these constructions extend to matrix coefficients on metaplectic covers of reductive groups, certain central extensions closely linked to reciprocity laws in number theory. These extensions often lead to surprising connections with combinatorial representation theory. Related developments in number theory, automorphic forms, and random matrix theory will also be discussed in an effort to stimulate new connections among these fields.
The conference will bring together a group of twenty international speakers who are leaders in the fields of number theory, automorphic forms, and combinatorial representation theory to discuss recent progress and suggest new directions of study. The conference program also aims to introduce a new generation of young mathematicians to these rapidly developing fields by offering some expository lectures, curating materials in an online website, and offering partial travel support for those without other sources of funding. A website for the conference may be found at math.mit.edu/~brubaker/bumpconf.html
The award funded a week-long conference at Stanford University (August 13-17, 2012) on the connections between automorphic forms, representation theory, and combinatorics. The program featured 21 internationally reknowned mathematical researchers, giving hour-long talks on a wide variety of cutting edge work in the above fields. They provided a blueprint for how each of the three fields can move forward in the coming decade, taking advantage of methodologies from the other two. The conference topics were chosen to celebrate the research to date of Daniel Bump, Professor at Stanford University. Professor Bump has been a leading mathematician in automorphic forms, representation theory and number theory for over three decades. Together with his many collaborators, he has contributed to a greater understanding of Whittaker functions, L-functions, the metaplectic group, and multiple Dirichlet series, with additional papers in such diverse areas as Toeplitz matrices, Voronoi-summation formulae, and exactly solved models in statistical mechanics. The conference talks revisited these works, discussed recent progress within them by Bump, his collaborators, and others, and suggested future open problems for the years to come. Conference funds not only subsidized the travel costs of speakers, but most importantly funded the participation of 17 graduate students from Boston College, Brown, Caltech, Columbia, UConn, MIT, Minnesota, Missouri, Princeton, SUNY Stony Brook, and Yale. These graduate students formed a lively cohort that actively participated in the lectures and subsequent discussions, asking questions and generating ideas for new projects. Participants in the conference were overwhelmingly positive about the scientific program and the benefit it provided to their research programs.
