Co-sponsored by the MSRI
(Mathematical Sciences Research Institute)
Francis Edward Su
June 6-9, 2005
Mathematical Sciences Research Institute
Berkeley, CARegistration Fee $250 by April 18,
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 from
them are primary examples. Other examples include arrangements of
points, lines, planes, convex
sets, and their intersection 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,
geometry. We will have fun visualizing polytopes and other
constructions, and exploring neat applications to
other fields such as the social sciences (e.g., fair division problems
and voting) and biology (e.g., the space of phylogenetic trees).
problems in geometric combinatorics are easy to explain, but remain
unsolved. 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. Participants will
receive some reading materials beforehand as well as some fun problems
in the field to whet their
appetite. For more information, please visit the workshop webpage
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