Mixed volumes

Tuesday, April 17, 2007 - 1:30pm - 2:20pm
Leonid Gurvits (Los Alamos National Laboratory)
Let K =(K1…Kn) be a n-tuple of
convex compact subsets in the Euclidean space
Rn, and let V (·) be the Euclidean volume in
Rn . The Minkowski polynomial
VK is defined as VK(x1,
…, xn)= V (λ1K1
+…+λnKn) and the mixed volume
V(K1,…,Kn) as

V(K1…Kn) =
n / ∂λ1…∂λn
Thursday, September 21, 2006 - 2:30pm - 3:20pm
Tien-Yien Li (Michigan State University)
Most recent algorithms for calculating the mixed volume of the
support A = (A1, ... , An ) of
a polynomial system P(x) = (
p1(x), ... , pn(x)) in
Cn by first finding all the fine mixed
in a fine mixed subdivision of A followed by adding the
volumes of all those cells will be presented in this talk. The
problem of finding all the fine mixed cells, which plays a
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