THE MALLAT FAMILY FUND FOR RESEARCH IN MATHEMATICS
invites you to a
SPECIAL LECTURE SERIES
to be presented by
The lectures will be held in
Technion - Israel Institute of Technology
The role of fundamental group in the topology of manifolds
In the first lecture, I will try to give some examples of manifolds and see how algebraic and analytic aspects of their fundamental groups are reflected both in their topology and in their geometry.We will see that in some sense, many key problems are largely independent of which manifold one considers with a given fundamental group.
Large Scale Methods
The theme here is redoing classical topology and geometric analysis on noncompact spaces, but with bounds on the size of problems and constructions. Fundamental groups are both replaced by and unified with metric spaces. The perspective enables us to get some information about nonsimply connected manifolds, but also gives informations about singularities.
Small Scale Consequences
Remarkably, the large scale structure of spaces forces some restrictions of what can occur infinitesimally. While this is hard to see for manifolds which are locally Euclidean by definition, it is quite easy to see for more complicated spaces.After developing such principles, we can prove a part of the picture suggested in Lecture I