A Murnaghan-Nakayama formula in quantum Schubert calculus

   The Murnaghan-Nakayama  rule expresses  the product  of a
Schur function with a Newton power sum in the basis of Schur
functions.   As  the  power  sums generate  the  algebra  of
symmetric  functions,  the  Murnaghan-Nakayama  rule  is  as
fundamental as  the Pieri rule.  Interesting,  the resulting
formulas from the  Murnaghan-Nakayama rule are significantly
more  compact  than  those   from  the  Pieri  formula.   In
practice,  it follows  from the  rule for  multiplying schur
functions for hook-shaped partitions.

In this talk,  I will discuss some background,  and then our
work  establishing  a  Murnaghan-Nakayama rule  for  quantum
Schubert polynomials,  which has been challenging.   This is
joint work with Morrison,   Benedetti, Bergeron, Colmenarejo,
and Saliola.