05.2018 veneziano amplitude and multiple zetas

The veneziano amplitude, the veneziano-shapiro amplitude, and multiple zeta values.

02.2018 bi-adjoint scalar tree amplitudes

A formula for bi-adjoint scalar tree amplitudes from fans of dual associahedra. Essentially a comment on the construction 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.

11.2017 notes on static spacetimes

The boundary value problem in general relativity, static spacetimes, and some Riemannian formulas for optics in static spacetimes.

09.2017 hilbert schemes of points notes

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.

05.2017 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.

04.2017 the reciprocity relation and static spacetimes

How many lorentz inner products you need to know 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

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.

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.

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.

problems for general relativity and cosmology: