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).

- "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.

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 |