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Mathematics Colloquium


Date:  Thursday, January 19, 2006

Title:  Integer Points and Rational Functions

Abstract:  Motivated by the formula for the sum of the geometric series, where a long polynomial sums up to a short rational function, we ask ourselves which sets of integer lattice points admit a short rational generating function. While examples include the sets of integer points in a rational polyhedron, lattice semigroups, and some other intreresting sets, the true extent of this phenomenon is still unknown (though there is a conjecture). The question turns out to have connections to continued fractions, Hilbert functions, and Presberger arithmetic. This is a survey talk.

Speaker:  Alexander Barvinok
Institution:  UM


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