Rhys Davies (Physics)

Except for this paragraph, and a change in title, this is a copy of my 'professional' website as it stood when I finished in academia. My EPSRC postdoctoral fellowship at Oxford finished in September 2013.
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Hodge numbers of Calabi–Yau threefolds

I have attempted to gather together all known pairs of Hodge numbers (h11, h21) of three-dimensional Calabi–Yau manifolds, and sorted them in two ways. In the first list, they are sorted first by h11, then h11+h21, and in the second list they are sorted first by h11+h21 and then by h11. The lists and associated references can be downloaded in this single zip file, or separately: list 1, list 2, references. I would like to acknowledge that I am building on the efforts of Philip Candelas, who collected together the majority of the existing data several years ago.

If you notice that I am missing any examples, please send me an email and I will add them. I have tried to provide at least one reference for each distinct manifold, but have not necessarily referenced all independent discoveries of particular manifolds.

Update

Previously, I had apologised here that the data was only available as plain text, rather than a proper database. This is no longer true, thanks to the efforts of Benjamin Jurke. His Calabi–Yau 3-fold Explorer allows you to search the list of known manifolds, and easily create pretty coloured plots, among other things.

By far the largest class of known Calabi–Yau threefolds are the hypersurfaces in toric fourfolds, constructed by Max Kreuzer and Harald Skarke. The data for these manifolds are also available in a separate database here.

Assorted notes

Disclaimer:

These notes are informal, and typically do not contain references. Although they all written by me, I do not claim that any of the material is original. They represent my understanding of the subjects, sometimes come to on my own, sometimes gained primarily from a single source, and sometimes drawn together from many sources.

Physics

F-theory/heterotic duality
F-theory is a relatively simple geometric way to describe certain non-perturbative supersymmetric backgrounds of type IIB string theory (at least, this is one way to look at it). Certain F-theory backgrounds have dual descriptions as heterotic string compactifications; these notes give a concise overview of this duality.
Millicharges and magnetic monopoles
Theories where the photon mixes with a 'hidden photon' generically contain particles with tiny electric charges. These notes explore the relationship between these particles, magnetic monopoles, and Dirac's charge quantisation argument.
Perturbation theory in atomic physics
A short overview of degenerate quantum perturbation theory, as applied to the structure of atoms. These were written to complement the B1 course at Oxford.

Mathematics

Spinor representations in dimensions up to eight
These notes go through the explicit construction of the various types of spinor representations (Dirac, Weyl, Majorana) of SO(D) for D between 2 and 8. The differences which occur for SO(D-1,1) are also briefly discussed.
The del Pezzo surface of degree 6
A description of several aspects of the geometry of the del Pezzo surface of degree 6, including its realisation(s) as a complete intersection in products of projective spaces, and as a toric surface, as well as calculations of its Hodge numbers and Kähler cone. I hope to tidy these notes up a bit when I find the time.
Complex geometry
Some elementary notes on complex and Kähler geometry, starting with the relevant linear algebraic concepts, such as the relationships between structures on a complex vector space and the underlying real vector space. These notes are very much a work in progress, but they may be of some small use in their current form.