I will introduce these two types of manifolds including basic definitions, properties, and applications.
Contact and Symplectic Manifolds
Apr. 15, 2014 1pm (MATH 220)
Grad Algebra/Logic
Jeffrey Shriner (CU Boulder)
X
A chip-firing game on a graph G begins with a configuration (the number of 'chips' on each vertex). When a vertex 'fires', it sends a chip to each adjacent vertex, so the only rule of the game is that a vertex may 'fire' if and only if it has at least deg(v) chips. We discuss a variant of the chip-firing game, called the dollar game, in which one vertex is required to always be in debt. Using the dollar game, we form an abelian group structure K(G), called the critical group of G. We compute the order of K(G), and look at how the dollar game may be used as a tool for analyzing the structure of the group.
The Dollar Game and the Critical Group of a Graph, Part 2
Contact and Symplectic Manifolds