Notes I have written
Representation Theory and Quantum Mechanics - Lie Groups, Lie Algebras, SU(2) and SO(3), Quantization, the Moment Map and Symmetries
Feynman's Theory of Superfluid Helium-4 - Multiparticle Wavefunction, Phonon Dispersion Curve, Vortex Lines (presented for Columbia physics seminar)
Crash Course in Statistical Mechanics - Entropy, Temperature, the Partition Function, Phase Transitions, Density Matrices and Entanglement Entropy
Crash Course in Black Holes - Relativity, Quantum Field Theory, Statistical Mechanics, Hawking Radiation and the Firewall Paradox (written for CS229)
Visualizing the Inverse Noether Theorem and Symplectic Geometry - Hamiltonian Mechanics, Vector Fields, Lie Bracket, Commutativity, Inverse Noether's Theorem, the Jacobi Identity, and fun pictures!
A Stroll Through Projective Geometry - RP1 and SL(2,R), the Cross Ratio, Steiner's Theorem, RP2, Projective Duality, Dual Curves, and many helpful pictures!
The Schwarzian Derivative and 2D CFT - Projective Space, the Cross Ratio, Möbius transformations and SO(1,3), Conformal Transformations, three ways to understand the Schwarzian Derivative, Ridge Systems, the Virasoro Algebra, and why the Schwarzian appears in 2D CFT! (Lecture notes for graduate theory seminar)
The C Metric for Beginners (with pictures) - The C Metric is a spacetime describing two charged black holes which are uniformly accelerated by a cosmic string. The notes start with a review of the Schwarzschild black hole and its Euclidean section, then give an introduction to the Lorentzian and Euclidean C metric. It then describes how the Euclidean C metric is an instanton describing the decay of a cosmic string via quantum tunneling, and how the Lorentzian C metric describes a vacuum transition from one asymptotically locally flat vacuum to another by a superrotation.