Spring 2018 Analysis Student Seminar

This semester, we will spend time defining and developing the basic properties of Loewner Theory, and its Stochastic Variant, Schramm-Loewner Evolution. Prerequisites are some familiarity with the core course material (Real Analysis I and II, Complex Analysis I).



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.





Sept. 12

Jack Burkart

Intro. Distortion Theorems for Conformal Mappings. Bieberbach Conjecture for n=2.

Contreras Section 1

Sept. 19

Matt Dannenberg

Convergence Results: Caratheodory Convergence, Hurwitz's Theorem, Herglotz Functions

Contreras Section 6.

Sept. 26

Ying Hong Tham

Loewner Chains Pt 1: Definition, Basic Properties, The Loewner PDE

Contreras Section 2

Oct. 3

Tim Alland

The Loewner ODE

Contreras Section 3

Oct. 10

Jack Burkart

Slit Domains and Chordal Theory

Contreas Sections 4 and 5

Oct. 17

Silvia Ghinassi

Probability: Rapid Introduction

Lawler Sections 1-6

Oct. 24

Jack Burkart

Probability: Examples, Martingales, Optional Stopping

Lawler Sections 1-6

Oct. 31

Matt Dannenberg

Brownian Motion: Construction and Basic Properties

Lawler Section 7

Nov. 7

Tim Alland

Stochastic Calculus: Pt. 1

Kemppainen Section 2.1-2.2.1

Nov. 14

Jack Burkart

Stochastic Calculus: Pt. 2

Kemppainen Section 2.2.2

Nov. 28

Jessica Maghakian

Stochastic Calculus: Pt. 3

Kemppainen Section 2.3 and 2.5

Dec. 5

Silvia Ghinassi

Schramm-Loewner Evolution: Pt. 1

Kemppainen Section 5.1

Dec. 12

Jae Ho Cho

Schramm Loewner Evolution: Pt. 2

Kemppainen 5.2, 5.2.2, 5.3.2