MSRI - Clay Mathematics Institute and MSRI Conference on Recent Progress in Dynamics

The scope of the conference will be fairly wide, but it will emphasize specific problems in dynamical systems, smooth ergodic theory, and related topics, including differential geometry, group theory and number theory, to name a few, that have seen much progress, but where significant problems vital to the field remain open. Specific examples are the Katok entropy rigidity conjecture for geodesic flows of negatively curved manifolds, the Boltzmann ergodic hypothesis, Liouvillean phenomena, the construction of metrics with ergodic geodesic flow, smooth rigidity of actions of abelian groups of higher rank.

This workshop will include a session to discuss open problems and to produce a list of these, with the intent of producing a concrete agenda for further research on several fronts. The following are some of the subjects related to dynamical systems that have seen outstanding advances recently, and that will be significant components of this workshop.

Billiards, and the question of their hyperbolicity and ergodicity.
The close relations between dynamical systems and differential (especially Riemannian) geometry.
The significant interactions that have developed between dynamical systems and number theory.
The extension of methods from the study of invariant measures for homogeneous and affine actions of higher rank abelian groups, initiated by Furstenberg's x2,x3-question, to other areas.
The study of actions of lattices in semisimple Lie groups.
The impact on statistical physics of Ruelle's work showing that a generalized Sinai--Ruelle--Bowen-state depends differentiably on the hyperbolic diffeomorphism for which it is defined.

The workshop will be held on the occasion of the 60th birthday of Anatole Katok. We will take this occasion to honor Katok during the conference for his significant influence on almost all areas in dynamical systems through his research, collaboration, teaching, organization and exposition.

This workshop is sponsored by the Clay Mathematical Institute and hosted by MSRI. It also benefits from generous contributions from Tufts University and the Pennsylvania State University.

Funding

To apply for funding, you must register by Tue, Jun 15 2004. Click to Register

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are made typically 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

Important

Additional Lodging information

Directions to MSRI

Schedule
Monday, September 27, 2004
9:30AM - 10:30AM	Gerhard Knieper	Hyperbolic Dynamics and Riemannian Geometry. [Video available]
1:35PM - 2:20PM	Mike Boyle	Symbolic Extension and Entropy Structure. [Video available]
2:30PM - 3:15PM	Dmitry Dolgopyat	Long time Asymptotics in Averaging. [Video available]
4:15PM - 5:15PM	Anatole Katok	Five Most Resistant Problems in Dynamics. [Video available]
Tuesday, September 28, 2004
9:00AM - 9:45AM	Danijela Damjanovic	Rigidity , KAM and other Methods. [Video available]
11:15AM - 12:00AM	David Fisher	Local Rigidity: Past, Present, Future. [Video available]
1:45PM - 2:30PM	Michael Jakobson	Parameter Exclusion and Markov Structure for Henon-like Families. [Video available]
2:40PM - 3:35PM	Manfred Einsiedler	Measure Rigidity of Higher Rank Actions. [Video available]
4:00PM - 4:45PM	Yuri Kifer	Averaging Revisited. [Video available]
Wednesday, September 29, 2004
9:55AM - 10:40AM	François Ledrappier	Horocycle Flow on Periodic Surfaces. [Video available]
11:15AM - 12:00AM	Marcelo Viana	The Zorich-Kontsevich Conjecture. [Video available]
1:45PM - 2:45PM	Bassam Fayad	On Area Preserving Disc Diffeomorphisms. [Video available]
2:50PM - 3:15PM	Stefano Luzzatto	The Lorenz Attractor is Mixing. [Video available]
3:15PM - 3:45PM	Andrew Torok	Statistical Limit Theorems for Suspension Flow. [Video available]
4:00PM - 4:20PM	Michael Field	Stability of Mixing and Rapid Mixing for Axiom A Flows. [Video available]
4:30PM - 4:55PM	Omri Sarig	Unique Ergodicity for Non-Uniquely Ergodic Systems. [Video available]
5:00PM - 5:40PM	Keith Burns	Stable Ergodicity. [Video available]
5:45PM - 6:00PM	Huyi Hu	Equilibriums of Some Non-Holder Potentials. [Video available]
Thursday, September 30, 2004
9:00AM - 9:45AM	Karl Schmidt	Isomorphism Rigidity. [Video available]
9:50AM - 10:35AM	Ralf Spatzier	Classifying Anosov Diffeomorphisms. [Video available]
11:00AM - 11:45AM	Steven Hurder	Rigidity of Compact Foliations. [Video available]
1:15PM - 2:00PM	James Yorke	Understanding Genomes Using Dynamical Systems. [Video available]
2:15PM - 3:00PM	Joerg Schmeling	Some Applications of Hitting Time Asymptotics -from Circle Covers to Dyadic Approximation. [Video available]
4:15PM - 5:00PM	Helmut Hofer	Facts and Problems in a more Quantitative Symplectic Geometry. [Video available]
Friday, October 01, 2004
9:00AM - 9:45AM	Domokos Szasz	Markov Approximations and Stochastic Properties of Billiards. [Video available]
9:50AM - 10:35AM	Jean-Paul Thouvenot	Quasi Simplicity and Disjointness. [Video available]
11:15AM - 12:00PM	Anton Zorich	Flat Surfaces. [Video available]
2:00PM - 2:45PM	Mark Pollicott	Self-Similiar Sets in the Plane with Positive Measure. [Video available]
2:50PM - 3:35PM	Michal Misiurewicz	Ergodic Natural Measures. [Video available]
4:10PM - 5:00PM	Sheldon Newhouse	Symbolic Extensions and Smooth System [Video available]

Questions about this workshop should be sent either by email to 267@msri.org
or by regular mail to:

Clay Mathematics Institute and MSRI Conference on Recent Progress in Dynamics Mathematical Sciences Research Institute 17 Gauss Way, Berkeley, CA 94720-5070. USA

The Institute is committed to the principles of Equal Opportunity and Affirmative Action.