Title: Introduction to Ito Calculus
Speaker: Nathan Hayford
Date/Time: Friday, October 8th, 2:00 pm
Abstract: The Ito calculus is at the foundation of the theory of stochastic PDEs. In this talk, I will introduce the calculus, and prove Ito’s lemma. I will then demonstrate how the theory of martingales + Ito’s lemma can be applied to derive deterministic equations for certain quantities appearing in the stochastic calculus. In particular, I will prove the conformal invariance of Brownian motion and the harmonic measure. If time permits, I will also start a discussion about Schramm-Loewner evolutions (SLEs).