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pop@ams.org |
Integer Points in Polyhedra, Geometry, Number Theory, Algebra, Optimization Sunday, July 13 - Thursday, July 17 Alexander
Barvinok, University of Michigan How many nonnegative integral solutions does a system of linear equations with integer coefficients have? Questions like the above have applications in a wealth of areas outside mathematics. At the same time, they appear in different disguises in various mathematical fields. For example, the original question has a number theoretical flavor. But in the view of a discrete geometer it "actually" asks for the number of lattice points in a polyhedron. In commutative algebra one would ask for the Hilbert series of a graded ring and in algebraic geometry for the Todd class of a toric variety. The (apparently simpler) question whether there is a solution at all is an integer linear optimization problem. The proposed conference focuses on these inner mathematical aspects of lattice points. The main motivation is to provide an opportunity to nurture and further develop the interaction between the disciplines. Our preliminary list of hour speakers includes Sylvain Cappell, Jeff Lagarias, Richard Stanley, Bernd Sturmfels, and Rekha Thomas. For further information please visit the conference website, at http://www.math.binghamton.edu/matthias/src.html. |
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