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>