Abstract:
A stability condition on a nodal curve \$X\$ is the assignment of integers to the nontrivial biconnected subcurves of \$X\$ satisfying some desired properties; equivalently, it is an assignment of integers to the biconnected subsets of vertices of a graph \$G\$, where \$G\$ is the graph dual to \$X\$. In this talk, we'll study the combinatorics of these stability conditions, and provide a construction of these stability conditions from subdivisions of the Lawrence polytope of the oriented cographic matroid \$M^*(G)\$ using the theory of single-element extensions of oriented matroids. We will also discuss connections to chip-firing on graphs through the theory of generalized break divisors. Finally, we'll discuss the limitations of our combinatorial approach, and some future directions of study.
Note: Please note the special location, Smith 205. There will be no pre-seminar. The main talk starts at 4:10.
Join Zoom Meeting: https://washington.zoom.us/j/
Meeting ID: 915 4733 5974