Title of the course: General Relativity for Mathematicians
Instructor: Prof. Alejandro Vilar López
Institution: University of British Columbia
Dates: 1-6 September 2025
Prerequisites: Basic differential geometry
Level: Advanced undergraduate
Abstract: The course will provide an introduction to the physics of General Relativity aimed at a mathematically oriented audience. Just assuming basic differential geometry, we will begin by introducing the causal structure of Lorentzian spacetimes. This will take us naturally to the (classical) definition of what a black hole is and a brief exploration of the surprising phenomena that occur in its presence. Depending on time and interest, some more advanced topics will be discussed in the final lectures: the initial value problem of General Relativity and its meaning as a dynamical system, the singularity theorems of Penrose and Hawking, and / or asymptotically AdS spaces and their connection to the AdS/CFT correspondence.
Language: English