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The cyclotomic polynomial, topologically.
Colloquium| Speaker: | Victor Reiner, University of Minnesota |
| Location: | 1147 MSB |
| Start time: | Thu, Jan 6 2011, 5:10PM |
(joint work with Gregg Musiker)
The cyclotomic polynomial is the minimal polynomial over the rational numbers Q satisfied by a primitive n-th root of unity. Its coefficients turn out to be integers, whose interpretation and signs are somewhat mysterious.
We will explain how to interpret these coefficients topologically, as computing the homology of certain simplicial complexes. The interpretation builds upon previous work (joint with Jeremy Martin) uncovering a strange connection between Q-bases for a cyclotomic extension of Q, and the higher dimensional spanning trees introduced by Gil Kalai and studied further by Ron Adin.
This connection is mediated by duality of coordinatized matroids, that is, the duality between Pluecker coordinates for Grassmannians of r-planes and (n-r)-planes in n-space. However, no previous experience with matroid duality or Grassmannians will be assumed in the talk.
Tea will be served in the Alder Room from 4:30-5:00