Minimal Free Resolutions of the toppling ideal of a graph and its initial ideal

Algebra Seminar
Monday, November 5, 2012 - 15:05
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
We describe minimal free resolutions of a lattice ideal associated with a graph and its initial ideal. These ideals are closely related to chip firing games and the Riemann-Roch theorem on graphs. Our motivations  are twofold:  describing information related to the Riemann-Roch theorem in terms of Betti numbers of the lattice ideal and the problem of explicit description of minimal free resolutions.  This talk is based on joint work with Frank-Olaf Schreyer and John Wilmes. Analogous results were simultaneously and independently obtained by Fatemeh Mohammadi  and Farbod Shokrieh.