
Percolation is a mathematical model for the filtering of a liquid through a porous material or the spread of a forest fire or an epidemic: the edges of some graph are declared open or closed depending on independent coin tosses, and then connected open clusters are studied. While simple to define, this model exhibits very complicated behavior, with non-trivial scaling exponents and dimensions.Centering on the 2D setting, we will discuss simple proofs of some important theorems, connection of percolation to other models,as well as remaining open questions. …

March 2-6, 2020
Sir Simon Donaldson
Stony Brook University Distinguished Professor of Mathematics
Xiuxiong Chen
An endowment made in the memory of Dr. John H. Marburger, III, former president of Stony Brook University, director of Brookhaven National Laboratory, science advisor to President George W. Bush, and Vice President for Research at Stony Brook, provides funding support for women undertaking advanced graduate study in the physical sciences, engineering, or mathematics.
Aleksander Doan is a Ph.D. candidate in the Department of Mathematics, working in the field of differential geometry. In his thesis, he studied the phenomenon of energy concentration for solutions to the equations of gauge theory, and explored a relationship between gauge theory and algebraic geometry.