Course - 32 aulas

Random spatial processes and percolative systems; Percolation: basic concepts and techniques I; Subcritical phase; Supercritical phase; Study of critical and near critical percolation; Russo-Seymour-Welsh technology; Two fundamental Kesten.s theorems; Cardy formula; Smirnov's theorem; Stochastic Loewner Evolution (SLE); Convergence to SLE(6); Locality property of SLE(6); Definition of SLE with the self-avoiding walk intuition; Restriction property of SLE(8/3); Restriction defect of the other SLEs; Phases of SLE; A measure on self-avoiding loops; Introduction to the Brownian loop soup via Wilson's algorithm; The Brownian loop-soup and SLE; Conformal Loop-ensembles; Conformal Loop-ensembles and SLE.