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Clay Mathematics Institute and MSRI Conference on Recent Progress in Dynamics September 27, 2004 - October 01, 2004
Registration Deadline: October 01, 2004 over 18 years ago
To apply for Funding you must register by: June 27, 2004 almost 19 years ago
Parent Program: --
Organizers Michael Brin, Boris Hasselblatt (chair), Gregory Margulis, Yakov Pesin, Peter Sarnak, Klaus Schmidt, Ralf Spatzier, Robert Zimmer

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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 theory of partially hyperbolic systems and nonuniformly hyperbolic systems. 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.
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Funding & Logistics Show All Collapse

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To apply for funding, you must register by the funding application deadline displayed above.

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

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MSRI does not hire an outside company to make hotel reservations for our workshop participants, or share the names and email addresses of our participants with an outside party. If you are contacted by a business that claims to represent MSRI and offers to book a hotel room for you, it is likely a scam. Please do not accept their services.

MSRI has preferred rates at the Hotel Shattuck Plaza, depending on room availability. Guests can call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Institute discount. To book online visit this page (the MSRI rate will automatically be applied).

MSRI has preferred rates at the Graduate Berkeley, depending on room availability. Reservations may be made by calling 510-845-8981. When making reservations, guests must request the MSRI preferred rate. Enter in the Promo Code MSRI123 (this code is not case sensitive).

MSRI has preferred rates at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select "Affiliated with the Space Sciences Lab, Lawrence Hall of Science or MSRI." When prompted for your UC Contact/Host, please list Chris Marshall (coord@msri.org).

MSRI has a preferred rates at Easton Hall and Gibbs Hall, depending on room availability. Guests can call the Reservations line at 510-204-0732 and ask for the MSRI- Mathematical Science Research Inst. rate. To book online visit this page, select "Request a Reservation" choose the dates you would like to stay and enter the code MSRI (this code is not case sensitive).

Additional lodging options may be found on our short term housing page.

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Schedule, Notes/Handouts & Videos
Show Schedule, Notes/Handouts & Videos
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Sep 27, 2004
09:30 AM - 10:30 AM
  Hyperbolic Dynamics and Riemannian Geometry.
Gerhard Knieper
01:35 PM - 02:20 PM
  Symbolic Extension and Entropy Structure.
Mike Boyle
02:30 PM - 03:15 PM
  Long time Asymptotics in Averaging.
Dmitry Dolgopyat
04:15 PM - 05:15 PM
  Five Most Resistant Problems in Dynamics.
Anatole Katok (Pennsylvania State University)
Sep 28, 2004
09:00 AM - 09:45 AM
  Rigidity , KAM and other Methods.
Danijela Damjanovic
11:15 AM - 12:00 AM
  Local Rigidity: Past, Present, Future.
David Fisher (Indiana University)
01:45 PM - 02:30 PM
  Parameter Exclusion and Markov Structure for Henon-like Families.
Michael Jakobson
02:40 PM - 03:35 PM
  Measure Rigidity of Higher Rank Actions.
Manfred Einsiedler (ETH Zürich)
04:00 PM - 04:45 PM
  Averaging Revisited.
Yuri Kifer (The Hebrew University of Jerusalem)
Sep 29, 2004
09:55 AM - 10:40 AM
  Horocycle Flow on Periodic Surfaces.
François Ledrappier (University of Notre Dame)
11:15 AM - 12:00 AM
  The Zorich-Kontsevich Conjecture.
Marcelo Viana (Institute of Pure and Applied Mathematics (IMPA))
01:45 PM - 02:45 PM
  On Area Preserving Disc Diffeomorphisms.
Bassam Fayad
02:50 PM - 03:15 PM
  The Lorenz Attractor is Mixing.
Stefano Luzzatto
03:15 PM - 03:45 PM
  Statistical Limit Theorems for Suspension Flow.
Andrew Torok
04:00 PM - 04:20 PM
  Stability of Mixing and Rapid Mixing for Axiom A Flows.
Michael Field
04:30 PM - 04:55 PM
  Unique Ergodicity for Non-Uniquely Ergodic Systems.
Omri Sarig
05:00 PM - 05:40 PM
  Stable Ergodicity.
Keith Burns (Northwestern University)
05:45 PM - 06:00 PM
  Equilibriums of Some Non-Holder Potentials.
Huyi Hu
Sep 30, 2004
09:00 AM - 09:45 AM
  Isomorphism Rigidity.
Karl Schmidt
09:50 AM - 10:35 AM
  Classifying Anosov Diffeomorphisms.
Ralf Spatzier (University of Michigan)
11:00 AM - 11:45 AM
  Rigidity of Compact Foliations.
Steven Hurder (University of Illinois at Chicago)
01:15 PM - 02:00 PM
  Understanding Genomes Using Dynamical Systems.
James Yorke
02:15 PM - 03:00 PM
  Some Applications of Hitting Time Asymptotics -from Circle Covers to Dyadic Approximation.
Joerg Schmeling
04:15 PM - 05:00 PM
  Facts and Problems in a more Quantitative Symplectic Geometry.
Helmut Hofer (Institute for Advanced Study)
Oct 01, 2004
09:00 AM - 09:45 AM
  Markov Approximations and Stochastic Properties of Billiards.
Domokos Szasz
09:50 AM - 10:35 AM
  Quasi Simplicity and Disjointness.
Jean-Paul Thouvenot
11:15 AM - 12:00 PM
  Flat Surfaces.
Anton Zorich (Institut de Mathematiques de Jussieu)
02:00 PM - 02:45 PM
  Self-Similiar Sets in the Plane with Positive Measure.
Mark Pollicott (University of Warwick)
02:50 PM - 03:35 PM
  Ergodic Natural Measures.
Michal Misiurewicz
04:10 PM - 05:00 PM
  Symbolic Extensions and Smooth System
Sheldon Newhouse