|Date: Monday, September 25, 2017
Location: 3866 East Hall (4:00 PM to 5:00 PM)
Title: An introduction to the critical group of a graph and discrete harmonic functions
Abstract: The critical group of a graph (also known as the sandpile group or Jacobian) is an abelian group associated to the graph which appears in a variety of contexts. Among other examples, versions of this group have arisen from the "sandpile" or "chip-firing" model of statistical physics, analogies with algebraic curves, and inverse problems on electrical networks.
In this talk, I'll introduce the critical group and give a brief survey of its different interpretations. I will then focus on some work done with David Jekel (UCLA) and others at the University of Washington REU, inspired by the electrical network angle, which helps uncover information about the graph hidden in the critical group. A description of the group as a space of "discrete harmonic functions" provides tools for computing critical groups of families of graphs, connecting the structure of the group to symmetry in the graph, and investigating a type of reducibility relevant to the inverse problem.
Speaker: Will Dana
Institution: University of Michigan