Title: Combinatorial geometries, convex polyhedra, and Schubert cells
| Speaker: | Cameron Marcott |
| Affiliation: | University of Waterloo |
| Room: | MC 6486 |
Abstract:
This is a reminder for our next meeting that will take place on Monday (June 29th) in MC6486.
Door will open at 4:15pm. As usual we will have 15 mins for socializing and for eating pizza before the talk starts (at 4:30pm sharp).
This paper illustrates the connections between matroid theory, algebraic geometry, and the theory of convex polytopes. A realization of a matroid of rank k on n elements is a point in the Grassmannian of k dimensional planes in n dimensional space. We obtain a stratification of the Grassmannian by looking at the sets of points corresponding to different realizable matroids. This stratification agrees with two other stratifications of the Grassmannian: one coming from a torus action and the other coming from permuted Schubert cells. To each cell, we may associate certain convex polytopes coming from the torus action and from the matroid defining the cell.
The
presentation
will
be
based
on
the
following
manuscript:
http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf
For
more
information
about
our
reading
group,
please
visit
our
webpage
http://www.math.uwaterloo.ca/~k2georgi/reading.htm