## Oliver Club

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.