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• 13:05-13:55 CG218 Panos Papazoglou (Oxford) Cutpoints of CAT(0) groups

It is known that if the boundary of a 1-ended hyperbolic group G has a local cut point then G splits over a 2-ended group. We prove a similar theorem for CAT(0) groups, namely that if a finite set of points separates the boundary of a 1-ended CAT(0) group G then G splits over a 2-ended group. Along the way we prove two results of independent interest: we show that continua separated by finite sets of points admit a tree-like decomposition and we show a splitting theorem for nesting actions on R-trees. This is joint work with Eric Swenson.

• 14:05-14:55 CG218 Mark Hagen (Cambridge) Hierarchically hyperbolic groups

I will discuss the class of hierarchically hyperbolic groups, which generalizes the class of hyperbolic groups and includes mapping class groups of surfaces, many cubical groups, and numerous other examples. The definition is modelled on the Masur-Minsky hierarchy machinery for mapping class groups, and I will illustrate it in the more concrete setting of right-angled Artin groups. I'll also discuss some applications of the theory to the large-scale geometry of the mapping class group and Teichmuller space of a surface.

15:00-16:00 common rom Tea

• 16:05-16:55 CM107 Caroline Series (Warwick) Continuous motions of limit sets

A Kleinian group is a discrete group of isometries of hyperbolic 3-space. Its limit set, contained in the Riemann sphere, is the set of accumulation points of any orbit. In particular the limit set of a hyperbolic surface group F is the unit circle.

If G is a Kleinian group abstractly isomorphic to F, there is an induced map, known as a Cannon-Thurston (CT) map, between their limit sets. More precisely, the CT-map is a continuous equivariant map from the unit circle into the Riemann sphere.

Suppose now F is fixed while G varies. We discuss work with Mahan Mj about the behaviour of the corresponding CT-maps, viewed as maps from the circle to the sphere. We explain how a simple criterion for the existence of a CT-map can be adapted to establish conditions on convergence of a sequence of groups G_n under which the corresponding sequence of CT-maps converges pointwise or uniformly to the expected limit. Very surprisingly, however, under certain circumstances even pointwise convergence may fail.

There will be an early dinner in Durham (further details to come).

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The Palatine Learning Centre is a new building between the maths department and Stockton Road. The cafe is at the end closest to the library (opposite to Law).

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