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
Note the unusual day
will speak on
Residual Eisenstein series and small automorphic representations
coming from string theory
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 <firstname.lastname@example.org>
Announcement from: Yaeli Malka <email@example.com>