CMI Workshop:
Geometry of Outer Space
October 19 – 22, 2009
The aim of this workshop is to bring together various researchers to study recent developments leading to a more geometric approach to Outer Space. The geometric aspects of Teichmueller theory have been lacking on the Outer space side, but the last couple of years seem to indicate that this is about to change and there is genuine hope for exciting progress. We plan to discuss various advances, make progress of stumbling blocks and identify key questions leading to further developments. Topics will include:
- The analog of Thurston's metric on Outer space (works of Handel-Mosher and Yael Algom-Kfir)
- The study of analytic properties of the boundary of Outer space (works of Ilya Kapovich and Ursula Hamenstaedt)
- The quest for the analog of the curve complex is in progress, the major obstacle being a proof of its hyperbolicity
- The study of intersection numbers (Guirardel's core)
The workshop will be held at the Clay Mathematics Institute headquarters; One Bow Street, Cambridge, Massachusetts.
Schedule
Monday, October 19
| 9:30-10:30 | Registration |
| 10:30-11:30 | Mladen Bestvina, The Lipschitz metric and another proof of the train track theorem |
| 12:00:2:00 | Lunch |
| 2:00-3:00 | Martin Bridson, Actions of mapping class groups and Aut(Fn) on CAT(0) spaces |
| 3:30-4:30 | Ruth Charney, Toward Outer Space for Right-angled Artin groups |
Tuesday, October 20
| 10:00-11:00 | Karen Vogtmann, The sphere system model of outer space |
| 11:30-12:30 | Michael Handel, Subgroup classification in Out(Fn) |
| 12:30-2:00 | Lunch |
| 2:00-3:00 | Ilya Kapovich, Generalized currents on free groups |
| 3:30-4:30 | Matt Clay, Twisting out fully irreducible automorphisms |
Wednesday, October 21
| 10:00-11:00 | Mark Feighn, A hyperbolic Out(Fn)-complex |
| 11:30-12:30 | Juan Souto, Automorphisms of the free splitting graph |
| 12:30-2:00 | Lunch |
| 2:00-3:00 | Ursula Hamenstaedt, Geometry of outer space as seen from the boundary |
| 3:30-4:30 | Yael Algom Kfir, The asymmetry of the Lipschitz metric |
Thursday, October 22
| 9:00-10:00 | Dan Margalit, Generating the hyperelliptic Torelli group |
| 10:30-11:30 | Alexandra Pettet, Current twisting and nonsingular matrices |
| 11:30-12:45 | Lunch |
| 12:45-1:45 | Kasra Rafi, The Teichmuller diameter of the thick part of moduli space |
| 2:15-3:15 | Vincent Guirardel, Purely irreducible normal subgroups of Out(Fn) and of the Mapping Class Group |
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