Abstract: Bernoulli percolation is a stochastic process originally introduced to model the flow
of fluid through a porous medium. Despite its very simple definition, it has turned out
to be one of the most interesting models in probability theory of the last half century. Three Fields
medals (Werner, Smirnov, Duminil-Copin) were awarded in the last 20 years for work directly
connected to percolation. The most dramatic progress has been on the 2 dimensional version
of the model.
In this talk, I will quickly review the basics of percolation, and then discuss critical percolation
in high dimensions (d \ge 6 if you are physicist, d \ge 11 if you want proofs).
In particular, I will then discuss some recent and ongoing work with Chatterjee and Hanson
on critical and near-critical scaling exponents and the distribution of the chemical distance.