Notes

This is a collection of personal notes on various topics related to my research. These aren't meant to be pedagogical, but rather as a means of writing to learn. I make no claims of originality nor correctness -- proceed with caution.

Analysis

1. PDEs

1.1: Sobolev Spaces

1.2: Smooth Approximations in Sobolev Spaces

1.3: Sobolev Inequalities

1.4: Trace Operators

2. Calculus of Variations

2.1: Euler-Lagrange Equations

2.2: Vanishing Lemmas

3. Gradient Flows

3.1: The JKO Scheme

3.2: Wasserstein Gradient Flows

4. Measure Theory

4.1: Set Algebras

4.2: Construction of Measures

4.3: Radon Measures and Topological Duals

Machine Learning

1. Stein Methods

1.1: Stein Operators and Stein Disrepancies