Schedule: July 15 to July 19 (5 classes), all at 16h00 (BRT)/19h00 (UTC). One must attend at least 4 classes to receive a certificate.
Workload: 10h
Topics: Symmetries and groups in fundamental physics. Lorentz and Poincaré groups. Maps between manifolds and diffeomorphisms. Lie derivative. Conformal infinity in Minkowski spacetime. Asymptotically flat spacetimes. Carrollian structure of conformal infinity. Symmetries of conformal infinity and the BMS group. Applications.
Pre-requisites: A standard introductory course in general relativity.
Bibliography:
These are the main references for the course. A complete list of references is available in the lecture notes.
Robert M. Wald. General Relativity. Chicago: The University of Chicago Press, 1984.
Stephen W. Hawking e George F. R. Ellis. The Large Scale Structure of Spacetime. Cambridge Monographs on Mathematical Physics. Cambridge: Cambridge University Press, 1973.
Andrew Strominger. Lectures on the Infrared Structure of Gravity and Gauge Theory. Princeton: Princeton University Press, 2018. arXiv: 1703.05448 [hep-th].
Lecture Notes (Extended Version): Aguiar Alves, Níckolas de. 2025. “Lectures on the Bondi–Metzner–Sachs group and related topics in infrared physics.” arXiv: 2504.12521 [gr-qc].