Student Analysis

Past Events

May
17
Date11:00 AM
Location
384I
Speaker
Josef Greilhuber (Stanford)

We will discuss applications of the clean composition calculus.

May
10
Date11:00 AM
Location
384I
Speaker
Ethan Lu (Stanford)

We will discuss the clean composition calculus of Guillemin and Duistermaat.

May
03
Date11:00 AM
Location
384I
Speaker
Yuefeng Song (Stanford)

Abstract

Apr
26
Date11:00 AM
Location
384I
Speaker
Selim Amar (Stanford)

We will move from the local to the global theory of FIOs, providing invariant definitions of relevant notions such as operator symbols. The necessary tools from symplectic geometry will be introduced. If time permits, we'll begin considering some applications.

Apr
19
Date11:00 AM
Location
384I
Speaker
Andy Yin (Stanford)

In this talk, we follow the book ‘Fourier Integral Operators’ by Duistermaat. Fourier integral operators (FIO) are a class of operators that generalise pseudodifferential operators. While pseudodifferential operators include solution operators to elliptic problems, FIO include solution operators…

Mar
18
Date2:30 PM
Location
384I
Speaker
Romain Jaques Higham Speciel (Stanford)

We will derive the transport equation as the second term in our approach to solving hyperbolic PDEs, describe the meaning of this equation from our symplectic perspective, and, if time permits, outline a solution strategy.

Mar
11
Date2:30 PM
Location
384I
Speaker
John Anderson (Stanford)

In this talk, I will continue to describe aspects of geometric optics, one of the main themes introduced earlier.  I also hope to describe a bit more about how this relates to some interesting properties of hyperbolic PDE.  In particular, I hope to motivate a bit more about why you may…

Mar
04
Date2:30 PM
Location
384I
Speaker
Andy Yin (Stanford)

Continuing from last week, we cover Chapter 1 of ‘Semiclassical Analysis’ by Guillemin and Sternberg. We are interested in solving a hyperbolic linear partial differential equation involving a time variable. We reduce it to an ‘eikonal equation’, which we can solve locally by finding a…

Feb
26
Date2:30 PM
Location
384I
Speaker
Josef Greilhuber (Stanford)

We will kick off our reading of Guillemin and Sternberg's monumental set of lecture notes about "Semiclassical Analysis", with a discussion of the textbook's introduction, and some additional motivating examples. Among these will be another "proof" of the Weyl law, as well as a "Weyl law" for…

Feb
12
Date2:30 PM
Location
384I
Speaker
Jared Marx-Kuo (Stanford University)