Many of the questions are of classical interest. Recently, applications such as computer graphics and robotics have provided new challenges for the discipline. A broad range of classical combinatorial techniques, from enumeration and extremal set theory to probabilistic methods, have been found useful in geometric combinatorics. In recent years powerful algebraic and topological tools have been applied successfully as well. This trend has led to a re-examination of classical geometry in the light of current mathematical techniques.
Lattice points in polytopes.
Application of methods of commutative algebra and algebraic geometry. Realization spaces of polytopes and point configurations. Oriented matroids and hyperplane arrangements. Enumeration of faces in polytopes, complexes and arrangements. Program Schedule and List of Speakers and Abstracts are available.