Description
Title: Standard monomials, matroids, and lattice paths.
Time: 7pm IST, gate opens 6:45pm IST.
Google meet link: meet.google.com/cbv-twjd-vno.
Phone: (US) +1 401-764-4238 PIN: 316 692 499#
Speaker Raman Sanyal, Goethe-Universität Frankfurt.
Abstract: Every finite collection of points is the set of solutions to
some system of polynomial equations. This is a (computationally)
reasonable representation, in particular when writing down defining
equations is easier than the actual points. Motivated by Grobner basis
theory for finite point
configurations, I will discuss standard complexes of 0/1-point
configurations. For a matroid basis configuration, the corresponding
standard complex is a subcomplexes of the independence complex, which is
invariant under matroid duality. For the lexicographic term order, the
standard complexes satisfy a deletion-contraction-type recurrence. For
lattice path matroids these complexes can be explicitly described in terms
of lattice path combinatorics. The talk is based on work with Alexander
Engstrom and Christian Stump.