Automorphic forms are a basic yet intricate structure in modern mathematics. Though historically they have been studied primarily by number theorists and representation theorists, they have connections to other branches of science. This research explores a number of questions connecting different areas of mathematics and physics. The project includes collaborative work with mathematical physicists that uses automorphic forms to describe corrections to general relativity that arise in string theory.
Other projects include a detailed investigation of the square-integrability of certain Eisenstein residues (which has applications to the unitary dual problem), as well as a study of Eisenstein series on infinite-dimensional Kac-Moody group (in particular, the meromorphic continuation of their constant terms). Another project concerns applications of Voronoi-style summation formulas to number theory, such as to subconvexity problems for automorphic L-functions. Finally, the Miatello-Wallach conjecture (that the moderate growth condition in the theory of automorphic forms is in fact redundant on higher rank groups) will also be a focus of the research.
