This semester, we will spend time defining and developing the basic properties of Brownian motion, and then move on to its connections to harmonic analysis (i.e solving the Dirichlet problem), harmonic measure, and develop some stocahstic calculus at the end time permitting.
Date 
Speaker 
Topic 
Reading 

Jan. 31 
Jack Burkart 
Introduction and Definition 
[BP] 6.16.2 
Feb. 7 
Jack Burkart 
Levy's Construction of Brownian Motion 
[BP] 6.2 
Feb. 14 
Matt Dannenberg 
Scaling Relations, Nowhere Differentiability, Holder Continuity 
[BP]6.3 
Feb. 21 
Ben Sokolowsky 
Reflection, Conformal Invariance, The Strong Markov Property 
[BP] 6.6,7.9 
Feb. 28 
Silvia Ghinassi 
Dimension Results 
[BP]6.4, 7.1 
Mar. 7 
Snow Day 

[BP] 6.10 
Mar. 14 
Spring Break  
Mar. 21 
Snow Day 

[BP] 7.2 
Mar. 28 
Snow Day 
[BP] 

Apr. 4 
Matt Dannenberg 
Law of Iterated Logarithm, Skorokhod's Representation, and Donkster's Invariance Principle 
[BP] 7.27.3 
Apr. 11 
Ben Sokolowsky and Jack Burkart 
Probabilistic View of Harmonic Functions 
[BP] 7.57.7 
Apr. 18 
Mu Zhao 
Conditional Probability and Martingales 
[La1] Ch. 6 
Apr. 25 
Jack Burkart 
Harmonic Measure and Kakutani's Theorem 
[GM], [BP] 7.9 
May 1 
Matt Dannenberg 
Intro to Stochastic Calculus 
[La2] 