Integer points in polyhedra. Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics

June 11 - June 15, 2006

Snowbird, UT

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.

Principal speakers

Karen Aardal
(Centrum voor Wiskunde en Informatica
& Eindhoven Institute of Technology)
Lattice reformulation of integer programming problems
Alexander Barvinok
(University of Michigan)
Efficient integer point counting in large dimensions
Sara Billey
(University of Washington)
Flag arrangements and triangulations of products of simplices
Persi Diaconis
(Stanford University)
Importance sampling versus Markov chains; a survey
Alain Lascoux
(Universite de Marne-la-Vallee)
Rational functions associated to the classical groups

Conference organizers

Matthias Beck (San Francisco State University)
Christian Haase (Freie Universität Berlin)
Bruce Reznick (University of Illinois, Urbana-Champaign)
Michèle Vergne (École Polytechnique Paris)
Volkmar Welker (Philipps-Universität Marburg)
Ruriko Yoshida (Duke University)


List of participants
Schedule of talks
Conference library
Conference pictures
Weather in Snowbird
General Joint Summer Research Conferences information