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Polynomial Equations and Convex Polytopes

Year of Award: 1999

Publication Information: The American Mathematical Monthly, vol. 105, 1998, pp. 907-922

Summary: This article considers the common zeros of d polynomials in d unknowns, generalizing the well-known results (like Descartes' rule of signs) that bound the zeros of a single polynomial in one variable. An important tool in this exploration is the connection between polynomials and convex polytopes. The paper further explains how many new results on the connection between polynomials and polytopes have created considerable excitement in late years.

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About the Author: (from The American Mathematical Monthly, vol. 105 (1998) Bernd Sturmfels received his Ph.D. in 1987 at the University of Washington under the supervision of Victor Klee. After postdoctoral years in Minneapolis and Linz, Austria, he taught at Cornell University for six years, before moving permanently to UC Berkeley. Sturmfels has been a Sloan Fellow, an NSF National Young Investigator, and a David and Lucile Packard Fellow. He has authored five books and 90 research articles in combinatorics, computational algebra, and algebraic geometry. With his wife, Hyungsook, and two young children, Nina and Pascal, he spent the academic year 1997-98 in Kyoto, Japan.

 

Author (old format): 
Bernd Sturmfels
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Bernd Sturmfels
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Publication Date: 
Tuesday, September 23, 2008
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Summary: 
This article considers the common zeros of d polynomials in d unknowns, generalizing the well-known results (like Descartes' rule of signs) that bound the zeros of a single polynomial in one variable. An important tool in this exploration is the connection between polynomials and convex polytopes. The paper further explains how many new results on the connection between polynomials and polytopes have created considerable excitement in late years.

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