Notes

This is an evolving collection of personal notes on various topics. They are not intended to be pedagogical, may be incomplete, and may contain errors. If you notice an error or would like to discuss something here, feel free to reach out!

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: The Cylindrical Sigma-Algebra

4.4: Pettis and Bochner Integrals

4.5: Radon Measures and Topological Duals

5. Functional Analysis

5.1: Operator Classes

5.2: Covariance Operators and Weak Moments

Machine Learning

1. Stein Methods

1.1: Stein Operators and Stein Disrepancies

2. Kernel Methods

2.1: Hilbert-Schmidt Independence Criterion