Spring 2018 Analysis Student Seminar

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.



All talks will be given in 5-127 on Wednesdays at 4:00, and we'll try to end around 5:15. The following is the tentative schedule, along with the references we will follow that day.





Jan. 31

Jack Burkart

Introduction and Definition

[BP] 6.1-6.2

Feb. 7

Jack Burkart

Levy's Construction of Brownian Motion

[BP] 6.2

Feb. 14

Matt Dannenberg

Scaling Relations, Nowhere Differentiability, Holder Continuity


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

Zeros of Brownian Motion Snow

[BP] 6.10

Mar. 14

Spring Break

Mar. 21

Snow Day

Law of the Iterated Logarithm Snow

[BP] 7.2

Mar. 28

Snow Day

Connections to Harmonic Functions pt. 1 Snow


Apr. 4

Matt Dannenberg

Law of Iterated Logarithm, Skorokhod's Representation, and Donkster's Invariance Principle

[BP] 7.2-7.3

Apr. 11

Ben Sokolowsky and Jack Burkart

Probabilistic View of Harmonic Functions

[BP] 7.5-7.7

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