THE REES DISTINGUISHED LECTURER SERIES
May 14, 2008
3:30 – 4:30 pm
304 Gore Hall
Talk for undergraduates
TITLE: The Abelian Sandpile Model
Professor Laszlo Babai
Department of Computer Science and Department of Mathematics
The University of Chicago
ABSTRACT
The Abelian Sandpile Model is a diffusion process on the grid, the analysis of which has fascinated physicists, mathematicians, and computer scientists for two decades.
The process under consideration starts with an empty checkerboard and puts "grains of sand" successively on selected "sites" (cells). When the "pile" at a site has 4 grains, it "topples," passing a grain across each side of the cell. (In the case of boundary cells, one or two grains fall off the board.) Some neighbor may now have acquired 4 grains; we repeat the process until the configuration stabilizes ("avalanche"). Then we add another grain at some site and start all over.
This process was introduced in 1988 by Bak, Tang, and Wiesenfeld as a model of the phenomenon of "self-organized criticality" in statistical physics. The evolution of the system is a "visual feast" (Creutz, 1991), and the dynamics gives rise to remarkable mathematical structure (Dhar, 1990).
After a general introduction, I will outline recent work I have done with Igor Gorodezky who was an undergraduate at the time; our collaboration started during a summer REU.
I will conclude with open p aspects of the model.
May 16, 2008
3:30 – 4:30 pm
304 Gore Hall
Talk for general mathematical audience
TITLE: Symmetry and Structure of Finite Graphs
Professor Laszlo Babai
Department of Computer Science and Department of Mathematics
The University of Chicago
ABSTRACT
Mild assumptions of symmetry often have a striking effect on the structure of a graph. A graph is "vertex-transitive" if all vertices are equivalent under automorphisms. We shall discuss implications of the assumption of vertex-transitivity on the connectivity, isoperimetry, growth, and other parameters of the graph; and mention applications to group theory, probability theory, number theory, the analysis of algorithms, and differential geometry.
No familiarity with graph theory is assumed.