I am open to supervising graduate-level reading courses in the general areas of partial differential equations, geometric analysis, and general relativity. Topics do not have to be closely related to my research interests; though the closer the topic is to my main research expertise the closer I can provide supervision and guidance to the reading course.
For a reading course we will typically meet 1--2 hours per week (more if necessary). Reading courses are student-guided; I will suggest a general framework and topics to study, you will read the material and give me a presentation on your progress. I will ask lots of questions to ensure your understanding.
Topics of previous reading courses supervised
- (Spring 2020) semi-Riemannian geometry
- Course follows B. O'Neill's Semi-Riemannian Geometry, with emphasis on what happens outside the Riemannian and Lorentzian case.
- (Fall 2018) self-gravitating, relativistic fluid dynamics.
- Course began with some basics concerning general relativity, fluid dynamics, and their reductions in warped-product symmetry. This is followed by hands-on research by the students on stability of spatially-homogeneous solutions of Einstein-Euler system in warped-product symmetry, under small non-homogeneous perturbations.
- (Spring 2018) semi-Riemannian geometry and general relativity.
- Course follows V. Schlue's lecture notes in GR and B. O'Neill's Semi-Riemannian Geometry (chapters 1--6, portions of 12 and 14).
- (Fall 2016) wave equations.
- Course consists an introduction of linear and nonlinear wave equations, and follows Chapters 1 and 2 of C. Sogge's Nonlinear wave equations.