For more information about this meeting, contact Anatole Katok, Robin Enderle.
| Title: | An Introduction to Teichm\"uller dynamics; this talk will continue at the special session on Wednesday at 4:40pm |
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| Seminar: | Working Seminar: Dynamics and its Working Tools |
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| Speaker: | Giovanni Forni, University of Maryland |
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| Abstract: |
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| We plan an introduction to Teichmueller dynamics from the point
of view of complex analytic geometry and Hodge theory. We will
describe the moduli space of holomorphic Abelian and quadratic differentials or, equivalently, of translation surfaces with
conical singularities. In particular, we will introduce several
structures on the moduli space (period map coordinates,
affine structure, canonical measures, $SL(2,R)$-action,
Teichmueller flow). We will then introduce the Hodge inner
product and explain how to use it to derive conclusion about
the Lyapunov spectrum of the Teichmueller flow. We will state
without proof the main theorems in Teichmueller dynamics
(Masur and Veech theorems about the finiteness of canonical
measures, the ergodicy and mixing of Teichmueller flow, etc.)
and an application to the dynamics of IET's (Masur and Veech proof
of the Keane conjecture). Time permitting we would like to
at least sketch somewhat different proofs of ergodicity of the Teichmueller flow with respect to a general class of invariant
measures and a proof of the Keane conjecture based on the local
uniform hyperbolicity of the Hodge norm under the Teichmueller flow.
This talk will continue at the special session on Wednesday at 3:35pm |
Room Reservation Information
| Room Number: | MB216 |
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| Date: | 03 / 20 / 2012 |
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| Time: | 03:30pm - 06:00pm |
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