Linearity in combinatorics and topology

Daniel Biss

University of Chicago

October 9,
4:15pm
refreshments at 3:45pm
2-338

ABSTRACT 

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.

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.


Speaker's Contact Info: daniel(at-sign)math.mit.edu


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