Studying Percolation on Infinite Graphs

May 28, 2008

Murray Elder of the University of Queensland knows Cayley graphs—arrays of edges and vertices that encode the algebraic structures of groups. He is also interested in percolation on such graphs. 

"Percolation is an idea that comes from physics and is currently a hot topic in pure mathematics," Elder says. The term percolation, he notes, "is used when infinite clusters form in the graphs, similar to water flowing through coffee grounds to form a pot of coffee."

Elder recently participated in a workshop devoted to "percolation on transitive graphs," held at the American Institute of Mathematics (AIM), in Palo Alto, Calif. The workshop brought together mathematicians working in geometric group theory, probability, and dynamics to exchange ideas and develop tools for solving some persistent open problems in the field.

"This research is maths for maths sake, but like all cutting edge research you don't always know where you will end up," Elder observes. "That's part of the beauty of it."

He also urges math students to seek opportunities to take part in such workshops. These venues offer participants chances to both learn about and contribute to research in particular fields and to establish new international collaborations to tackle important problems.

"The satisfaction and opportunities that these types of workshops provide students with is what being a mathematician is all about," Elder says.

Source: University of Queensland, May 7, 2008.