A Murnaghan-Nakayama formula in quantum Schubert calculus

   The  Murnaghan-Nakayama formula  expresses  the  product of  a
Schur function  with a  Newton power  sum in  the basis  of Schur
functions.   In geometry,  a Murnaghan-Nakayama  formula computes
the  intersection of  Schubert cycles  with tautological  classes
coming from the Chern character.  In previous work with Morrison,
we establshed a Murnaghan-Nakayama formula in the cohomology of a
flag variety and conjectured a version for the quantum cohomology
ring of  the flag  variety.  In  this talk,  I will  discuss some
background, and  then some  recent work proving  this conjecture.
This  is joint  work with  Benedetti, Bergeron,  Colmenarejo, and
Saliola.