{TALK 
        {"October 9}
        {"Linearity in combinatorics and topology}
        {"Daniel Biss}
        {"University of Chicago}
        {"daniel@math.mit.edu}
        {"

The marriage between combinatorics and topology has been a long and
fruitful one.  There is, however, one notable exception, namely the lack
of a combinatorial model for the local structure present in smooth
manifolds.  The first stumbling block has been the difficulty of
finding a combinatorial way of capturing the linear algebraic apparatus
present in the tangent bundle.  The most successful approach turns out to
rely on the language of oriented matroids.
<p>
I will explain what oriented matroids are and how they enter the study of
manifolds.  After sketching recent progress in this direction, I will
then present several tantalizingly open-ended questions.  The talk should
be accessible to those unfamiliar in both oriented matroids and smooth
manifolds.

}
}