I am a researcher working in the mathematical physics group at the Mathematical Institute. I am working on dualities of string and field theories, as well as compactifications of string theory. This involves a whole lot of fascinating mathematics, in particular (algebraic) geometry.
My upbringing as a student has been as a theoretical particle physicist. As things go, I first got involved with string theory and then with the mathematics needed to make progress.
In slightly technical terms, I have worked a lot on F-theory, which is a very elegant geometrization of the $SL(2,Z)$ self-duality of type IIB string theory. This works by replacing the complexified string coupling of type IIB string theory by a elliptic curve (i.e. a torus), and nicely ties together M-Theory, type IIB string theory and heterotic E8 x E8 string theory. A basic introduction can be found here: http://people.sissa.it/~cecotti/FNOTES10.pdf
Although this is great fun in its own right and has led to many insights, F-Theory provides an interesting starting point for 'string phenomenology'. This concerns the question how we should think about string theory in relation to the known low energy physics as described by the Standard Models of particle physics and cosmology. A review of why F-theory is interesting for string phenomenology can be found here: http://arxiv.org/abs/1009.3497.
String Theory is a very beautiful theory which seems to be unique as a 10 dimensional theory, but it is presently unclear how we should think about it in relation to our four-dimensional world. An obvious way to reconcile 10 with 4 is to consider solutions of string theory which effectively look four-dimensional below a certain energy scale. One of the fundamental problems of String Theory is that there are a huge number of possibilities to do this. Although opinions on what this means differ wildly, it is fair to say that many things about this 'landscape' are poorly understood. Here are a few questions:
- Can we find a solution of String Theory which perfectly reproduces observed physics ?
- Is the set of effectively four-dimensional solutions finite or does it become finite once we impose additional restrictions ?
- Is every consistent four-dimensional theory an effective description of some string theory compactification ?
- Is (a well-defined subset of) every consistent four-dimensional theory an effective description of some string theory compactification ?
- Do the solutions of String Theory have universal features (maybe upon demanding additional restrictions) ?
- Are there correlations between (desirable) features ?
- What has cosmological evolution to say about all this ?
Attacking such questions requires a fair deal of interesting mathematics to be developed.
Recently, I have worked a lot on manifolds of 'exceptional holonomy' which only exist in dimension 7 (holonomy $G_2$) and 8 (holonomy $Spin(7)$). These are fairly special and intriguing geometries, the existence of which is tightly linked to exciting physics: compactifications of M-Theory (or 11dimensional supergravity) on such spaces gives theories in four and three dimensions with minimal supersymmetry. It is hence very interesting to understand constructions and properties of such spaces, which is, however, a hard problem in mathematics. By probing such spaces with various string theories and exploiting dualities between different string compactifications, we have nevertheless been able to make substantial progress in the last two years (and there is plently left to do).
+44 1865 615181
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Discrete Symmetries of Calabi-Yau Hypersurfaces in Toric Four-Folds
COMMUNICATIONS IN MATHEMATICAL PHYSICS issue 3 volume 360 page 935-984 (June 2018) Full text available
Compact, singular G(2)-holonomy manifolds and M/heterotic/F-theory duality
JOURNAL OF HIGH ENERGY PHYSICS issue 4 (23 April 2018) Full text available
Heterotic line bundle models on elliptically fibered Calabi-Yau three-folds
JOURNAL OF HIGH ENERGY PHYSICS issue 4 volume 2018 (16 April 2018) Full text available
Towards generalized mirror symmetry for twisted connected sum G
Journal of High Energy Physics issue 3 volume 2018 (1 March 2018)
Tops as building blocks for G
Journal of High Energy Physics issue 10 volume 2017 (1 October 2017)
- compactifications of String/M-theory and the resulting effective field theories
- Calabi-Yau manifolds (in complex dimensions 1 to 4)
- $G_2$ manifolds
- geometry and string dualities
- singularities and the associated physics
- mirror symmetry
I like music a lot and often listen to resonance.fm while working. If I had to pick one, my favourite movie would be 'Night on Earth' by Jim Jarmusch, but it is hard to choose. I am a Linux fanboy. My favourite colour is blue. In the late summer, I like to hunt for wild mushrooms, but won't tell you where to find them (secret of the trade). I like cacti and coriander. We live in a pretty big universe.
Here are some lectures I have recently given on how to use the open-source mathematics software sage (http://www.sagemath.org/) to do computations with Calabi-Yau manifolds: http://www.mth.kcl.ac.uk/~ss299/GGI/scheduleSchool.html