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.

References

Schedule

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.

Date

Speaker

Topic

Reading

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

[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

Jack Burkart

Zeros of Brownian Motion

[BP] 6.10

Mar. 14

Spring Break

Mar. 21

TBA

Law of the Iterated Logarithm

[BP] 7.2

Mar. 28

TBA

Connections to Harmonic Functions pt. 1

[BP]

Apr. 4

TBA

Connections to Harmonic Functions pt. 2

[BP] 7.5-7.7, 7.10

Apr. 11

TBA

Martingales and Conditional Probability

[La1]

Apr. 18

TBA

Harmonic Measure and Kakutani's Theorem

[GM], [BP] 7.9

Apr. 25

TBA

Intro to Stochastic Calculus pt. 1

[La2]

May 1

TBA

Intro to Stochastic Calculus pt. 2

[La2]