Analysis Student Seminar

from Friday
June 01, 2018 to Monday
December 31, 2018
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Instructions for subscribing to Stony Brook Math Department Calendars

Wednesday
September 12, 2018

4:00 PM
Math Tower 5-127
Jack Burkart, Stony Brook University
Intro. Distortion Theorems for Conformal Maps

Before we get to SLE, we will introduce ideas and motivation behind classical Loewner theory. In particular, we will discuss its relationship to the Bieberbach conjecture.

We will also prove classical distortion theorems for conformal maps that we will need in the upcoming weeks, including the Koebe 1/4 theorem and the Koebe distortion theorem.


Wednesday
September 19, 2018

4:00 PM
Math Tower 5-127
Matthew Dannenberg, Stony Brook University
Caratheodory Convergence, Herglotz Representation, and Hurwitz's Theorem

We will give a characterization of convergence of conformal mappings in terms of convegence of image domains (for some appropriate notion of convergence).

To conclude our prerequisites, we will prove are Hurwitz's theorem that says a sequence of conformal maps converging locally uniformally is conformal or constant, and the Herglotz Representation formula for harmonic functions.


Wednesday
September 26, 2018

4:00 PM
Math Tower 5-127
Ying Hong Tham, Stony Brook University
Loewner Chains and the Loewner PDE

We will define radial Loewner chains, and describe their various convergence and distortion properties using the tools from the previous weeks.

We will also derive the Loewner PDE, and as an application, prove the Bieberbach conjecture for the case n=3.


Wednesday
October 03, 2018

4:00 PM
Math Tower 5-127
Tim Alland, Stony Brook University
The Loewner Differential Equation


Wednesday
October 10, 2018

4:00 PM
Math Tower 5-127
Jack Burkart, Stony Brook University
Slit Domains and Chordal Loewner Theory


Wednesday
October 17, 2018

4:00 PM
Math Tower 5-127
Silvia Ghinassi, Stony Brook University
Intro to Probability

We will quickly discuss and compare the vocabulary of probability theory with that of measure theory. Then we will introduce independence and conditional expectation.


Wednesday
October 24, 2018

4:00 PM
Math Tower 5-127
Jack Burkart, Stony Brook University
Optional stopping time and examples

Last week after a quick review of probability we introduced conditional expectations, martingales and stopping times. We will talk about optional stopping times and complete the picture with examples.


Wednesday
October 31, 2018

4:00 PM
Math Tower 5-127
Matthew Dannenberg, Stony Brook University
Brownian Motion

In this talk we will define Brownian motion carefully, discuss its construction, and discuss many of its useful properties, including the Markov property and its scaling limit properties.


Wednesday
November 14, 2018

4:00 PM
Math Tower 5-127
Jack Burkart, Stony Brook University
Stochastic Calculus Pt. 2

We'll discuss the Stochastic integral as a continuous time martingale.


Wednesday
November 28, 2018

4:00 PM
Math Tower 5-127
Jessica Maghakian, Stony Brook University
Ito's Formula and Stochastic Differential Equations

We state and prove Ito's formula and define Stochastic differential equations and state an existence/uniqueness result for them.


Wednesday
December 05, 2018

4:00 PM
Math Tower 5-127
Silvia Ghinassi, Stony Brook University
SLE: Definition and Basic Properties

We will define SLE two ways and discuss some of the basic properties it satisfies.


Wednesday
December 12, 2018

4:00 PM
Math Tower 5-127
Jae Ho Cho, Stony Brook University
SLE: Transition from simple curves to non-simple curves

To finish up the semester, we discuss the proof that SLE$(\kappa)$ transitions from being a simple curve to a nonsimple curve when $\kappa = 4$.


Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars