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Workshop:
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Sunday May 23 through Thursday May 27, 2004
at the Mathematical Sciences Research Institute, Berkeley, CA
Geometric Combinatorics refers to a growing body of mathematics concerned with counting properties of geometric objects described by a finite set of building blocks. Polytopes (which are bounded polyhedra) and complexes built up form them are primary examples. Other examples include arrangements of points, lines, planes, convex sets, and their intersectin patterns. There are many connections to linear algebra, discrete mathematics, analysis, and topology, and there are exciting applications to game theory, computer science, and biology. The beautiful yet accessible ideas in geometric combinatorics are perfect for enriching courses in these areas.
The target audience is professors who desire to learn about this exciting field, enrich a variety of courses with new examples and applications, or teach a stand-alone course in geometric combinatorics.
Some of the topics we will cover include the geometry and combinatorics of polytopes, triangulations, combinatorial fixed point theorems, set intersection theorems, combinatorial convexity, lattice point counting, and tropical geometry. We will also explore applications to other fields such as the social sciences (e.g., fair division problems) and biology (e.g., the space of phylogenetic trees). Some of the material will reflect recent research trends from the Fall 2003 program at MSRI in this field.
Familiarity with linear algebra and discrete mathematics will be assumed for some of the topics considered.