Arick Shao 邵崇哲

Research / Expositions

This page contains other material geared toward exposing topics related to my research areas to a wider mathematical audience.

Workshops and Conferences

Here are some workshops/conferences that I helped to organize.

Workshop on Geometric Hyperbolic PDE

This was a small workshop aimed at exposing young researchers in the London and surrounding areas to geometric wave equations. A major goal is to foster connections with other areas of mathematics, such as general relativity and spectral theory.

The workshop was headlined by mini-courses by professors Sergiu Klainerman and Maciej Zworski and complemented by talks by several young researchers highlighting some recent developments in the field.

Survey Notes and Presentations

The section contains media from survey presentations I have given.

Uniqueness Theorems for Waves from Infinity

Below are slides from talks surveying some of my recent results (with various collaborators) regarding uniqueness problems for linear and nonlinear wave equations with data at infinity.

Nonlinear Wave Equations

The following are lecture notes from a graduate course I co-taught in fall 2015. Based on select parts of the lecture notes by Sigmund Selberg and the book Nonlinear Dispersive Equations by Terence Tao, the notes cover some of the classical theory behind linear and nonlinear wave equations.

  1. ODEs and Connections to Evolution Equations (.pdf) (01/2016)
  2. Linear Wave Equations (.pdf) (01/2016)
  3. Nonlinear Wave Equations: Classical Existence and Uniqueness (.pdf) (01/2016)
  4. Nonlinear Wave Equations: Vector Field Methods, Global and Long-time Existence (.pdf) (01/2016)

The above are a more complete version of previous notes (Original 01/2014) on similar topics, based on a few graduate-level talks I gave at the University of Toronto in fall 2012 and fall 2013.

A Brief Introduction to Mathematical Relativity

Below are short notes and presentation slides from talks I have given which introduced the field of mathematical relativity. The exposition focuses on explaining the mathematics behind various commonly mentioned aspects of special and general relativity, such as the twin paradox, the big bang, and black holes. The material is kept deliberately brief and is presented in an informal way; while helpful, no background in differential geometry or partial differential equations is required.

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