Some real and unreal conjectures in enumerative geometry

Frank Sottile

University of Massachusetts - Amherst


   Recent progress on the question of when a problem in 
enumerative geometry may have all of its solutions be real
has been stimulated by some remarkable conjectures of Shapiro
and Shapiro, which are false in their original generality.
However, they fail in a very interesting way.

  This talk will describe some further conjectures in this 
area, including refinements of the conjectures of Shapiro
and Shapiro, and the very compelling evidence (both 
computational and theorems) in support of these new conjectures.