- Series
- Graph Theory Seminar
- Time
- Thursday, March 6, 2014 - 12:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Spencer Backman – Math, GT
- Organizer
- Robin Thomas
This talk is a sequel to the speaker's previous lecture given in
the January 31st Combinatorics Seminar, but attendance at the first talk is
not assumed. We begin by carefully reviewing our generalized cycle-cocyle
reversal system for partial graph orientations. A self contained
description of Baker and Norin's Riemann-Roch formula for graphs is given
using their original chip-firing language. We then explain how to
reinterpret and reprove this theorem using partial graph orientations. In
passing, the Baker-Norin rank of a partial orientation is shown to be one
less than the minimum number of directed paths which need to be reversed in
the generalized cycle-cocycle reversal system to produce an acyclic partial
orientation. We conclude with an overview of how these results extend to
the continuous setting of metric graphs (abstract tropical curves).