"Lower bounds for real solutions to systems of polynomials"

Around 2000, as part of their work on the Shapiro conjecture,
Eremenko and Gabrielov computed the topological degree of the
real Wronski map.  This was often positive, which established
a lower bound for the number of real solutions to certain
problems in the Schubert calculus.   Since then, there have
been many results establishing structure in the numbers
of real solutions, particularly lower bounds, for polynomial
systems with structure.

   My talk will discuss some of this work establishing lower
bounds that this work of Eremenko and Gabrielov engendered.