2017 notes on static spacetimes
the boundary value problem in general relativity; the definition of mass for static spacetimes; Riemannian techniques for studying optics in static spacetimes.

2017 seminar on analytic continuation of path integrals
and also…
2017 notes on analytic continuation of path integrals
Integrals via supersymmetric quantum mechanics; Witten’s cycles for the Feynman integral; relation to Floer; SQM on the loop space; large-radius limits and beta-gamma systems.

2017 introductory seminar on chy and klt

2017 quantum and floer cohomology: a basic example and the isomorphism
Three variations on the quantum cohomology of projective space (as prototype for all Kahler manifolds); Gromov-Witten, Mathai-Quillen, Floer homology and the ring structure.

2017 notes on hawking radiation and heat kernel expansions, in the style of the 1980s
The GR action, extrinsic curvature, and the thermal path integral; the laplacian on a circle, zeta determinants, relation to heat kernels, asymptotic expansion of heat kernels on compact mflds, laplacian on an interval, heat kernels for mflds with boundary.

2016 gravitational memory
Null infinity, integrating Einstein’s equations, geodesic deviation. Weinberg’s soft factorisation and loop corrections. Gravitational memory and the mass aspect.

2014 covariant averages in general relativity and cosmology
Covariant averages. Some evolution equations. Reduction to Buchert’s equations. Appendices include technical remarks about ADM, Raychaudhuri, etc.

2014 hamiltonian systems and general relativity
Classical gauge systems and Dirac’s procedure. General relativity and its gauge freedoms. A presentation of shape dynamics.


relativity problems
For general relativity students. Super-radiance, gravitational waves, lensing, cosmology.

orthogonality in physics
For mathematical methods students; lecture notes about least squares, Sturm-Liouville, and the propagator of a free quantum particle.

mechanical motivations for geometry
Planets. Charged particles. And fluids.