Courses

This semester

Below are the courses I teach or have taught at UERJ. Each page contains the syllabus, bibliography, lecture notes, and problem sets.

Note: All courses are taught in Portuguese. Some course materials (lecture notes, problem sets) may be in Portuguese as well.

Five new graduate courses are in preparation, with no assigned semester yet. Their syllabi and draft lecture notes are in the Wiki:

Algebraic Structure of Quantum Field Theory — operator algebras, Tomita–Takesaki modular theory, and recent developments on crossed products and entanglement in QFT
Holography through Quantum Information and Operator Algebras — how the observables of a quantum theory can encode a spacetime: recoverable observables in small quantum systems, operator algebras and modular structure, continuum QFT, and the geometric dictionary
Generalized Symmetries and Topological Matter — from the lattice gauge theory classics to higher-form symmetries, anomalies, and topological order
Geometric QCD: a critical course on Migdal’s IAS lectures — Migdal’s geometric-QCD proposal studied through explicit calculations: loop equations, momentum variables, the proposed surface construction, Majorana theory, and the twistor spectrum
Statistical Physics of Neural Networks and Language Models — statistical mechanics as the way into neural networks and language models: how text becomes vectors, how attention combines them, and how training adjusts the parameters

The first three were designed with companion master’s-thesis projects — see the Students page.