Chip-firing via open covers

Series: 
Algebra Seminar
Monday, August 26, 2013 - 15:00
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Georgia Institute of Technology
,  
 Chip-firing on graphs is a simple process with suprising connections to various areas of mathematics.  In recent years it has been recognized as a combinatorial language for describing linear equivalence of divisors on graphs and tropical curves.  There are two distinct chip-firing games: the unconstrained chip-firing game of Baker and Norine and the Abelian sandpile model of Bak, Tang, and Weisenfled, which are related by a duality very close to Riemann-Roch theory.  In this talk we introduce generalized chip-firing dynamics via open covers which provide a fine interpolation between these two previously studied models.