Campuses:

Gale

Thursday, September 21, 2006 - 9:30am - 10:20am
Frank Sottile (Texas A & M University)
In 1980, Askold Khovanskii established his fewnomial bound for
the number of
real solutions to a system of polynomials, thereby showing that
the complexity
of real solutions to a polynomial system depends upon the number
of monomials
and not the degree. This fundamental finiteness result in real
algebraic
geometry was proven by induction on the number of monomials and
the bound is
unrealistically large.

I will report on joint work with Frederic Bihan on a new
fewnomial bound which
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