Notes

Here are some expository notes I have written on various topics in mathematics and theoretical physics, many of them lecture notes or slides for journal club talks. None of them contain original material, except for any mistakes. Corrections and comments are always welcome, and can be emailed to me.

Physics Notes

• Gravitational Path Integrals: a set of lecture notes on some basic topics in semiclassical quantum gravity. [UNDER CONSTRUCTION!]
• 2D CFT and the Conformal Bootstrap: an introduction to conformal field theory in 2 dimensions.
• Chern-Simons Theory in a Knotshell: a review of some aspects of abelian and non-abelian Chern-Simons theory.
• 2D Euclidean Quantum Gravity: an exploration of the moduli space of Riemann surfaces, its intersection theory, and its relation to quantum gravity (see also the talk). [UNDER CONSTRUCTION!]
• Covariant Phase Space: the CPS formalism and relativistic Hamiltonian field theory (see also the talk).
• Universal Spectrum of 2D CFT: a talk on modular invariance and some universal semiclassical features of holographic 2D CFTs, and their relationship to the Hawking-Page transition in 3D gravity.
• Disentangling Entanglement Entropy: a talk on the replica trick and the entropy of an interval in 2D CFT.
• Renormalizing the Renormalization Group: notes for a talk on Wilsonian renormalization, RG flow, the Callan-Symanzik equation, CFTs, and the space of QFTs from a nonperturbative, geometrical perspective.
• Self-Force and Radiation Reaction: a talk on subtle self-effects in classical electromagnetism.
• AdS/Cold Atoms: AMO physics, the Schrödinger equation, and holographic duality (see also the talk).
• FM spectroscopy: a talk on phase modulation and laser locking in AMO physics.
• The Hubbard Model: an undergraduate thesis written under Prof. Sebastian Will.

Math Notes

• Elliptic Functions and Abelian Integrals: a talk on local function theory and meromorphic forms on tori.
• Galois Cohomology and the Weak Mordell-Weil Theorem: notes for a talk on some algebraic and p-adic technology for understanding elliptic curves over number fields.
• Representations of S_n and the Gelfand-Tsetlin Basis: notes on the representation theory of the symmetric group.
• Projective Geometry: notes for a talk on geometry in the spirit of Felix Klein's Erlangen program.
• A Field Guide to Linear Algebra: vector spaces, linear operators, inner products, and the spectral theorem.
• False Theorems and Fake Proofs: notes for a talk given to high school students through Splash.