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                Department of Mathematical Sciences
                   The Johns Hopkins University

                              SEMINAR

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James F. Lawrence                                 October 25, 2001
Department of Mathematics                         304 Whitehead Hall
George Mason University                           Refreshments: 3:30 p.m.
                                                  Seminar: 4:00 p.m.

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              SOME PROBLEMS OF COMBINATORIAL GEOMETRY


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                               ABSTRACT


There are multitudes of interesting and apparently difficult 
problems relating to the combinatorics of convex sets.  We discuss 
open questions involving enumeration of faces of polytopes, problems 
associated with the convexity theorems of Radon and Tverberg, and
questions concerning the crossing numbers of complete graphs and
their generalizations to higher dimensions.  Some of these questions
are considered in the setting provided by oriented matroids.


There are multitudes of interesting and apparently difficult
problems relating to the combinatorics of convex sets.
We discuss open questions involving enumeration of faces of
polytopes, problems associated with the convexity theorems of Radon
and Tverberg, and questions concerning the crossing numbers of complete
graphs and their generalizations to higher dimensions.
Some of these questions are considered in the setting provided
by oriented matroids.