The twenty-second meeting of the North British Mathematical
Physics Seminar was held on **Saturday 18 October
2008** in Durham, in the Derman Christopherson Room of the Calman Early
Learning Centre, next to the Department of
Mathematical Sciences. These
people came.

10:30-11:15

Coffee

11:15-11:40

Pau Figueras
(Durham)

In this talk I will review the recent developments in generating
stationary axisymmetric solutions of five-dimensional Einstein's
equations. I will explain in some detail how to obtain the black
saturn
and the doubly spinning ring using the inverse scattering method for
gravity. As a further development, I will show how these techniques
can be
combined with the SL(3,R) transformations to generate a black ring in
Taub-NUT.

11:45-12:40

Mukund Rangamani
(Durham)

Holography for non-relativistic CFTs

12:45-14:00

Lunch

14:00-14:55

Christian Korff
(Glasgow)

Recently there has been interest in so-called non-Hermitian
quantum systems and the question under what circumstances such
systems allow for the explicit construction of an inner
product which renders the quantum Hamiltonian Hermitian. We
apply this discussion to the U_q(sl_2)-invariant anisotropic
Heisenberg chain and show using techniques from representation
theory that the Hamiltonian can be made Hermitian w.r.t. to a
particular scalar product which we explicitly construct for
special values of q on the unit circle. These values are of
special interest as it has been argued in the literature that
the QG invariant Heisenberg chain and its algebraic features
are closely related to similar stuctures in logarithmic CFT
(LCFT). We make contact with this discussion for q^2=-1 which
ought to correspond to the simplest LCFT with c=-2.

15:00-15:25

Jamie Parsons
(Durham)

The lightest black hole (in 2+1 D)

15:30-16:15

Tea

16:15-17:10

Govind Krishnaswami
(Durham)

Multi-matrix models are toy-models for gluon dynamics in quantum
non-abelian gauge theories, such as Yang-Mills theory. They also appear in
models for quantum gravity and various combinatorial problems. The 't
Hooft limit as the matrices become large is a `classical' limit and
expected to be a good starting point for an approximation method. However,
determining the limiting correlations is itself difficult and requires
further approximations. We present a variational principle for Euclidean
large-N matrix models. It can be regarded as a classical action for a
discrete model of closed string field theory. It involves the confluence
of ideas on the entropy of operator-valued random variables and the
cohomology of automorphism groups of tensor algebras.

Patrick Dorey
Last modified: 19 October 2008