Quantum Reality:  Rational curves in real Grassmannians

Frank Sottile
University of Massachusetts at Amherst

   Inspired by theoretical physics and to a lesser extent by
linear systems theory, mathematicians have recently developed
sophisticated techniques (quantum cohomology) to treat enumerative 
geometric questions about curves in many spaces.  In the 
important case of rational curves in a Grassmannian, elementary 
geometric arguments which generalize classical techniques of 
Schubert and Pieri from the 19th century suffice to treat these 
problems.  Rather surprisingly, these same elementary arguments 
show that these geometric problems may have all solutions be real.

  This talk will describe how to obtain real number solutions to
this geometric concerning rational curves on a Grassmannian.  We 
begin with a concrete description of a rational curve on the 
Grassmannian and some motivation for this problem from systems 
theory, and then present an elementary derivation of the number 
of solutions which also shows how all solutions can be real.