A special North British Mathematical Physics Seminar will be held on Wednesday **7 April 2010** in Edinburgh in the guise of a minisymposium on The Mathematics of String Theory, part of a combined British Mathematical and Applied Mathematical Colloquia taking place in Edinburgh from 6 to 9 April.

9:00-9:30

Sanjaye Ramgoolam
(Queen Mary, London)

I describe how the Feynman diagram calculation of one-Matrix Model correlators can be expressed in terms of the counting of equivalence classes of triples of permutations, which are related to counting of holomorphic maps from string worldsheets defined over the closure of rationals and to Dessins d'Enfants. The absolute Galois group organizes the Feynman diagrams into orbits. Correlators of multi-matrix models are related to edge colorings of the Dessins, which provide a useful tool to describe known Galois invariants and to define new ones.

9:30-10:00

Amihay Hanany
(Imperial College, London)

Brane Tilings give a large class of SCFT's in 3+1 and 2+1 dimensions. In this talk I will discuss several attempts to classify all such models. Special attention will be devoted to the class of Abelian orbifolds of ℂ³ and of ℂ⁴. Statistical properties of these models can be derived using some techniques in crystallography and in number theory.

10:00-10:30

James Lucietti
(Imperial College, London)

The study of black hole solutions to higher dimensional versions of Einstein's equations is motivated by string theory and more recently by the gauge/gravity correspondence. It turns out that in higher dimensions there is a much richer set of possible black holes as compared to the classic case of four space-time dimensions. I will give a brief overview of our current (lack of) knowledge in this area, with particular emphasis on the black hole uniqueness/classification problem. I will then discuss recent progress on the classification of extremal black holes -- these are a class of black holes of special importance in string theory and the gauge/gravity correspondence.

10:30-11:00

Jan Gutowski
(King's College, London)

Considerable advances have been made in the analysis of supersymmetric solutions associated with string theory. New techniques in spinorial geometry, developed with G. Papadopoulos and U. Gran, can be applied to the classification of supersymmetric black hole near-horizon geometries in higher dimensional supergravity. Such solutions are of particular interest, as black hole uniqueness theorems in four dimensions do not extend to higher dimensions. I will describe, based on the paper arXiv:1001.2460 [hep-th], how these techniques can be used to classify all supersymmetric black hole near-horizon geometries in heterotic supergravity, and some new solutions with novel geometries will be presented.

11:00-11:30

Coffee

11:30-15:00

Discussion, Lunch,...

15:00-15:30

Carlos Núñez
(Swansea)

I will summarise some recent progress in the duality between gauge fields and strings. A connection between previously known string backgrounds will be presented, together with new backgrounds and its field theory duals.

15:30-16:00

Chris Hull
(Imperial College, London)

Generalised geometry and double geometry are discussed and compared, and their applications to string theory and T-duality are considered.

16:00-16:30

Tea

17:00-17:30

Nick Dorey
(DAMTP, Cambridge)

I will review the role of integrability in recent progress in understanding string theory on Anti-de Sitter spaces and its duality to planar gauge theory.

If you wish to attend the meeting, or for further questions, please email Richard Szabo. Limited funds are available to help with travel expenses of participants with no other source of funding. We hope that this will encourage postgraduate students and postdocs to attend the meeting. Please book early to take advantage of the cheaper train fares!

The venue will be in the Appleton Tower, a 15-minute walk from Waverley station. The morning session will be in Lecture Theatre 2 and the afternoon session in Lecture Theatre 3.

Train information can be obtained from here.

Partial support for this and other NBMPS meetings comes from the London Mathematical Society via a Scheme 3 grant. In addition, exceptionally for this meeting, we are also supported by a grant from the The Mathematical and Theoretical Physics Group of the Institute of Physics.

José Figueroa-O'Farrill
Last modified: 18 Mar 2010 at 22:22 GMT