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Frank Sottile University of Massachusetts-Amherst Invited Talk, Solving Systems of Polynomial Equations, |
It is a difficult problem to say anything meaningful about the number of real solutions to a system of equations. Recently, Eremenko and Gabrielov introduced a notion, that of the real degree of a projection map, that can give a non-trivial lower bound on the number of real solutions to some systems of polynomial equations.
In this talk, I will describe this idea of Eremenko and Gabrielov,
give some applications, and discuss its limitations. In addition, I
will show how this degree may be computed for some projections of some
toric varieties.