Automorphic Forms, Representations, and Combinatorics

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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