For a generic system of n polynomials in n variables over the complex numbers, Bezout's theorem bounds the number D of common zeros (in the algebraic n-torus) by the product of the degrees of their homogenizations in P^n. Notice that if all degrees are chosen higher than some fixed prime, say, this bound becomes unwieldy as n grows larger. We will have an example-oriented discussion of the Bernstein-Kushnirenko-Khovanskii (BKK) Theorem, which gives the optimal upper bound on D, with equality for sufficiently generic systems. Speaker(s): Robert Walker (University of Michigan)
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