30.05.2018 veneziano amplitude and multiple zetas
The veneziano amplitude, the veneziano-shaprio amplitude, and multiple zeta values.
12.02.2018 [arXiv:1802.03384] bi-adjoint scalar tree amplitudes
A formula for bi-adjoint scalar tree amplitudes based on dual associahedra. Essentially inspired by, and a mild development of, the ideas in [arxiv:1711.09102].
09.12.2017 notes on spin fields and their correlators
The construction of spin fields (which go back to Freed-Martinec-Shenker) and its relation to repn theory. Formulas for spin fields correlators (work by Schlotterer et. al.).
30.11.2017 some notes on ambitwistor spaces
Some generalities about spaces of null geodesics and some concrete examples for flat space using pure spinors. And a summary of various stuff from the 1980s.
27.11.2017 notes on static spacetimes
The boundary value problem in general relativity, static spacetimes, and some Riemannian formulas for optics in static spacetimes.
30.11.2017 [Oxford] seminar on analytic continuation of path integrals
WKB solving of Schrodinger’s equation, Stoke’s rays, and representing integrals using supersymmetric Quantum Mechanics on the half-line.
8.06.2017 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.
25.05.2017 [Oxford] 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.
6.04.2017 [Lyon] the reciprocity relation and static spacetimes
An off-the-cuff lecture to answer the following question: how much information do you need in order to work out the ratio of the two volumes traced by a pencil of light rays that intersects two spatial hypersurfaces?
16.01.2017 [Oxford] 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.
14.06.2016 gravitational memory
Null infinity, integrating Einstein’s equations, and geodesic deviation. Weinberg’s soft theorem and loop corrections. Gravitational memory and the mass aspect.
25.05.2015 averages in general relativity and cosmology
Some evolution equations for averaged quantities and technical remarks about Arnowitt-Deser-Misner and the Raychaudhuri equation.
- warm-up problems,
- schwarzschild I,
- schwarzschild II,
- gravitational radiation I,
- gravitational radiation II,
- cosmology I,
- cosmology II.
2017 general relativity revision problems
Super-radiance, gravitational waves, lensing, and cosmology.