**THE MALLAT FAMILY FUND FOR RESEARCH IN MATHEMATICS **

**invites you to a**

**SPECIAL LECTURE SERIES**** **

**to be presented by**

Professor Yair Minsky

Yale University

The lectures will be held in

Room 232

Amado Mathematics Building

Technion - Israel Institute of Technology

Haifa, Israel

Lecture I: Monday 17 March, 2008 at 15:30

**Curve
complexes in geometry and topology**

The complex of curves on a surface, introduced by Harvey in the 70's, is a simplicial complex that encodes disjointness properties of simple closed curves. I will survey the role that this object has played recently in the study of mapping class groups, Teichmuller space, topology of 3-manifolds, and hyperbolic geometry.

Lecture II: Wednesday, 19 March, 2008 at 15:30

**Coarse
geometry of mapping class groups**

In the second lecture I will focus on the mapping class group of a surface S as a geometric object. This group can be studied by considering the interlocked structure of the collection of all curve complexes of subsurfaces of S. With this machinery a coarse picture can be obtained, and for example the geometric rank of the group can be shown to be equal to the maximal rank of an abelian subgroup.

Lecture III: Thursday, 20 March, 2008 at 15:30

**Quasi-isometric
rigidity of mapping class groups**

A group is quasi-isometrically rigid if any group quasi-isometric to it is equivalent to it up to the extraction of finite-index subgroups and quotients by finite subgroups. Hamenstadt and independently Behrstock-Kleiner-Minsky-Mosher recently established this property for mapping class groups. In the third lecture I will discuss this problem and some aspects of the proof.