- 14:00-15:00 CM107
**Pierre Will**(Institut Fourier, Grenoble)*On 2-generator subgroups of PU(2,1)* -
15:10-16:10 CM107
**Anna Pratoussevitch**(Liverpool)*Real Forms of Higher Spin Riemann Surfaces* -
16:30-17:30 CM107
**Jim Howie**(Heriot-Watt, Edinburgh. )*Weight of groups and surgery on knots*

12:30-13:45 lunch in ** The Court Inn**.
This is located on Court Lane (see the map ).

The group PU(2,1) is the isometry group of the complex hyperbolic plane. Discrete subgroups of PU(2,1) are thus natural generalisations of Fuchsian and Kleinian groups. In this talk, I will review a few known results about them and present recent progresses in their study.

We will describe the space of higher spin bundles on Klein surfaces, i.e. m-th roots of the cotangent bundle of a (hyperbolic) Riemann surface equipped with an anti-holomorphic involution. To this end we study representation of Fuchsian groups into the universal cover of the full isometry group of the hyperbolic plane. This result has applications to the classification of anti-holomorphic involutions on quasi-homogeneous surface singularities. This is joint work with S. Natanzon.

The weight of a group G is the smallest integer n such that some subset of size n generates G as a normal subgroup of itself. In particular, any n-knot group has weight 1 for any n, as it is the normal closure of a meridian element. Hence many problems arising from knot surgery reduce to questions about whether certain groups can have weight 1. I will talk about some interesting examples of such questions.

Room CM107 is on the ground floor, to the left from the main entrance.

There will be an early dinner in Durham. Please e-mail Anna Felikson if you want to attend.