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.  An  important generalization  of Schur  functions are
Schubert polynomials (both classical  and quantum).  For these, a
Murnaghan-Nakayama  formula  is   geometrically  meaningful.   In
previous work with Morrison,  we established a Murnaghan-Nakayama
formula  for  Schubert  polynomials  and  conjectured  a  quantum
version.  In this  talk, I will discuss some  background and then
some recent work proving this  quantum conjecture.  This is joint
work with Benedetti, Bergeron, Colmenarejo, and Saliola.