The Weizmann Institute of Science Faculty of Mathematics and Computer Science Algebraic Geometry and Representation Theory Seminar Seminar Room, Room 261, Ziskind Building on Tuesday, January 15, 2013 at 11:00 Note the unusual day Steve Miller Rutgers university will speak on Residual Eisenstein series and small automorphic representations coming from string theory Abstract: String theorists have investigated correction terms (in the low energy limit) to Einstein's general relativity in type IIB string theory. These are automorphic functions whose asymptotics they understand in terms of theories in higher dimensions. We recently identified some of these correction terms as residual Eisenstein series. This gives new information about which Feynman diagrams contribute to certain interactions. Furthermore, supersymmetry then makes nontrivial number theoretic predictions about these Eisenstein series, such as vanishing of Fourier coefficients. We proved a conjectured vanishing statement by showing the underlying automorphic representation attached to these Eisenstein series has a small wavefront set. (This generalizes work of Ginzburg-Rallis-Soudry on automorphic minimal representations, which itself proves an important special case of the supersymmetry prediction.) Finally, the physical intuition about asymptotics suggests these residues are square-integrable, consistent with a broader conjecture of Arthur about the unitarity of other "unipotent" representations. Extending the computations used in identifying the Eisenstein series, I have now shown the unitarity of each of the spherical representations of Chevalley groups in Arthur's conjecture (Annals of Math., to appear). Joint work with Michael Green and Pierre Vanhove. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Yaeli Malka <yaeli.malka@weizmann.ac.il>