- Series
- Dissertation Defense
- Time
- Friday, June 21, 2013 - 10:00am for 1.5 hours (actually 80 minutes)
- Location
- Skiles 005
- Speaker
- Farbod Shokrieh – School of Mathematics, Georgia Tech
- Organizer
- Farbod Shokrieh
Please Note: Advisor: Dr. Matthew Baker
We study various binomial and monomial ideals related to the theory of
divisors, orientations, and matroids on graphs. We use ideas from potential
theory on graphs and from the theory of Delaunay decompositions for lattices
to describe minimal polyhedral cellular free resolutions for these ideals.
We will show that the resolutions of all these ideals are closely related
and that their Betti tables coincide. As corollaries we give conceptual
proofs of conjectures and questions posed by Postnikov and Shapiro, by
Manjunath and Sturmfels, and by Perkinson, Perlman, and Wilmes. Various
other results related in the theory of chip-firing games on graphs --
including Merino's proof of Biggs' conjecture and Baker-Shokrieh's
characterization of reduced divisors in terms of potential theory -- also
follow immediately from our general techniques and results.