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).

References

"Loewner's Theory: A Parametric Method To Tackle Problems In Complex Analysis" by Contreras. Link here.
"Notes on Probability" by Lawler. Link here.
"Stochastic Loewner Evolution" by Zinsmeister. Link here.
"Schramm-Loewner Evolution" by Kemppainen. Link on this webpage.

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
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