March 27-29, 2006 -- 2:10 p.m.
All Lectures at the Fields Institute,
Yair Minsky (Yale)
Curve complexes, surfaces and 3-manifolds
The curve complex of a surface is a simplicial complex whose
structure encodes the disjointness relation among essentially
embedded circles. It is elementary to define but difficult to
analyze, and has recently played a central role in the solution
of problems in hyperbolic geometry, topology of 3-manifolds, and
mapping class groups of surfaces. I will survey these developments
and try to give a feeling for the kind of tools that they involve,
and the kind of open problems which remain.
The Fields Institute Coxeter Lecture Series (CLS) brings a leading
mathematician to the Institute to give a series of three lectures
in the field of the current thematic program. The first talk is
an overview for a general mathematical audience, postdoctoral
fellows and graduate students. The other two talks are chosen,
in collaboration with the organizers of the thematic program,
to target specialists in the field.