**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

Room
001

Technion - Israel Institute of Technology

**The role of fundamental group in the topology
of manifolds**

Lecture
I:

Room
001,

**Examples**

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.

Lecture
II:

Room
001,

**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.

Lecture
III:

Room
001,

**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