Current algebra asks a deceptively simple question: instead of building a many-body theory out of particles $c_{\mathbf k}, c^\dagger_{\mathbf k}$, can we build it out of the fluid variables — the densities and currents that experiments actually measure? For free fermions in one dimension the answer is the familiar $U(1)$ Kac–Moody algebra, but the standard derivation leans hard on a filled Fermi sea, a linearized dispersion and a momentum cutoff. This talk replaces that derivation with the Bjorken–Johnson–Low prescription, which extracts the equal-time commutator from the high-frequency tail of a correlation function and therefore never has to assume what the ground state looks like. Applied to the Hatsugai–Kohmoto (HK) model — an exactly solvable non-Fermi liquid that violates Luttinger’s theorem — the method shows that the natural low-energy objects are not bare currents but parton (holon/doublon) currents, that they close into an affine $\mathfrak{su}(2)$ algebra, and that a manifestly local Sugawara-type Hamiltonian built from them reproduces the HK equations of motion and two-body correlators in the infrared. The suggested moral: the notorious non-locality of the HK model may be an artifact of writing local degrees of freedom in non-local variables.

Lecture I of a two-part introduction to conformal field theory, told from the condensed-matter side. The organising question: a critical $\phi^4$ theory is strongly interacting and we cannot solve it — so what can symmetry alone tell us? The answer runs from the emergent scale invariance at a fixed point, through the conformal group and the correlators it fixes, to the operator product expansion and the bootstrap, where crossing symmetry plus unitarity pin the 3D Ising critical exponents to six digits without ever evaluating a path integral. A preview of radial quantization closes the session.

A three-part pedagogical tour: what a neural network actually is and how it is trained, what attention adds once the data are sequences, and how both are being used right now in many-body physics — neural-network wavefunction ansätze optimised by variational Monte Carlo, and reduced density matrices learned without the wavefunction at all. The organising claim: a network is a very flexible fitting function, and the physics lives entirely in the details of how much of it you build in by hand.

Xiao Wang (Cornell, Eun-Ah Kim group) introduces droplet dynamics — a compact spatial block of local excitations or defect insertions embedded in a much larger quantum background — and shows how it realizes a universal class of unconventional dynamical transitions, identified as dynamical Gross–Witten–Wadia transitions, in both the XX/free-fermion and transverse-field Ising chains.

The presentation argues that for modern physics research, the key question is no longer whether to use AI, but how to use it effectively. It distinguishes two major roles: NN-based AI for principles (neural-network fitting, neural quantum states, DeepH) and LLM-based AI for workflow (planning, memory, tools, APIs, MCP, agent loops).

These notes build the bulk–boundary correspondence of topological band insulators from the ground up — from the modern theory of polarization to the protected edge spectrum and the wider topological zoo. Both the typeset write-up and the original handwritten notes are attached below.