Integer points in polyhedra. Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics
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 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 question of whether a solution exists is an integer linear feasibility problem. In addition, the last decade saw many applications of lattice-point questions to seemingly distant fields such as Representation Theory, Statistics, and Computer Science.
This 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.
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Karen Aardal
(Centrum voor Wiskunde en Informatica & Eindhoven Institute of Technology) | Lattice reformulation of integer programming problems |
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Alexander Barvinok
(University of Michigan) | Efficient integer point counting in large dimensions |
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Sara Billey
(University of Washington) | Flag arrangements and triangulations of products of simplices |
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Persi Diaconis
(Stanford University) | Importance sampling versus Markov chains; a survey |
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Alain Lascoux
(Universite de Marne-la-Vallee) | Rational functions associated to the classical groups |