Geometric Bijections Between Spanning Trees and Break Divisors

Series: 
Combinatorics Seminar
Tuesday, April 7, 2015 - 12:05
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Georgia Tech
,  
Organizer: 
The Jacobian group Jac(G) of a finite graph G is a group whose cardinality is the number of spanning trees of G. G also has a tropical Jacobian which has the structure of a real torus; using the notion of break divisors, one can obtain a polyhedral decomposition of the tropical Jacobian where vertices and cells correspond to the elements of Jac(G) and the spanning trees of G respectively. In this talk I will give a combinatorial description to bijections coming from this geometric setting, I will also show some previously known bijections can be related to these geometric bijections. This is joint work with Matthew Baker.