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The aim of this mini-workshop, located at the department
of mathematics in Pisa, is to bring together researchers in
hyperbolic geometry and its ramifications. It will consist of three
series of lectures:
The lectures are aimed at graduate/postdoc students and research mathematicians with a general interest in topology and geometry. They will take place at the Aula Magna of the department of mathematics. Here is the timetable: |
|
| Wednesday 12 June | Thursday 13 June | |
| 10.00-11.00 | Brock | Sisto |
| 11.00-11.30 | - Coffee break - | - Coffee break - |
| 11.30-12.30 | Aramayona | Brock |
| 12.30-14.30 | ||
| 14.30-15.30 | Sisto | Aramayona |
| 15.30-16.00 | - Coffee break - | - Coffee break - |
| 16.00-17.00 | Brock | Sisto |
| 17.00-18.00 | Aramayona |
There is no registration fee. Those wishing to attend the workshop should send an e-mail to martelli at dm dot unipi dot it. Abstracts follow.
| Javier Aramayona |
Rigidity and mapping class groups |
After introducing mapping class groups and discussing some of their basic properties, we will study homomorphisms between mapping class groups. We will give a sketch proof of a celebrated theorem of Ivanov, stating that, provided the genus is high enough, every automorphism of the mapping class group is induced by a homeomorphism of the underlying surface. Finally, we will explore some known constructions and results about homomorphisms between mapping class groups of different surfaces. No prior knowledge of the subject will be assumed.
| Jeffrey Brock: |
Combinatorial Teichmuller theory |
An abstract will appear soon.
| Alessandro Sisto: |
Gromov boundaries and relative hyperbolicity |
Relatively hyperbolic groups are "modelled" on fundamental groups of finite volume hyperbolic manifolds, but they include many more examples. The theory of relatively hyperbolic groups has been used in the proof of the Virtual Haken Conjecture, and is often useful to prove properties of fundamental groups of 3-manifolds via geometrization. Fundamental groups of hyperbolic manifolds act on hyperbolic space and its boundary. Similarly, there is a notion of boundary of a relatively hyperbolic group. We will study its properties and apply them to show results about (metric) embeddings of relatively hyperbolic groups and 3-manifold groups.
We may cover some local expenses to phd/postdoc students (for instance, by taking care of their accomodation). If you are interested in that, write me an email. Here is a suggested list of hotels: please mention the conference at our math department when you book your room.
