April 24, 2014
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Spring 2006
Thematic Program on Holomorphic Dynamics, Laminations, and Hyperbolic Geometry


Bruce Kleiner (Michigan)
Mikhail Lyubich (Toronto and SUNY Stony Brook)
Yair Minsky (Yale)

Mike Shub (Toronto)
Michael Yampolsky (Toronto)

Scientific committee:

Yakov Eliashberg (Stanford)
David Gabai (Princeton)
Etienne Ghys (ENS de Lyon)
Francois Ledrappier (University of Notre Dame)
Mitsushiro Shishikura (Kyoto)
John Smillie (Cornell)
Dennis Sullivan (CUNY & SUNY Stony Brook)
Alberto Verjovsky (UNAM)

Overview of the program.

The main focus of this program will be on the interaction between 3-dimensional Hyperbolic Geometry and Holomorphic Dynamics. These two fields have flourished through the past 30 years, with numerous fruitful exchanges that have enriched both of them. In recent years, we have witnessed many exciting breakthroughs in the both fields. The program would provide an opportunity to reckon the recent achievements and to discuss further directions they open. Along with the above two main themes, we plan to incorporate into the program a number of related directions, including the theory of laminations, partially hyperbolic dynamics, and flows on moduli spaces. All of them are closely interconnected, in particular, through the theory of laminations which provides them with a unifying framework. Tentatively, the beginning of the program will concentrate on topics in partially hyperbolic dynamics, Teichmüller flow, and laminations, the middle part will focus on one- and two-dimensional holomorphic dynamics; and the end will cover various topics in hyperbolic geometry including the recent solution of longstanding conjectures in deformation theory of hyperbolic manifolds and recent advances in Thurston's Geometrization Program. Accordingly, the program will include two or three workshops and a number of graduate courses and mini-courses on the topics of the program.

Spring Activities:

Dynamical Systems Seminar
Mondays, 3:10 p.m. - Room 230
Mini Courses
Wednesdays, 1:30 p.m., Fridays, 1:30 p.m.(if needed) - Room 230
Computability and Complexity in Analysis and Dynamics Seminar
Fridays, 2:10 p.m. - Bahen Bldg., BA 026
Young People Dynamics Seminar
Friday at 5pm, Fields Library

January 5-9, 2006
Partially hyperbolic dynamics, laminations, and Teichmuller flow Workshop
Org. Cttee: G. Forni, M. Lyubich, C. Pugh, M. Shub

Jan 9-10-11, 2006
Distinguished Lectures by Gregory Margulis

March 7-11, 2006
Holomorphic dynamics Workshop
In celebration of John Milnor's 75th birthday
Org. Cttee: M. Lyubich, J. Smillie, M. Yampolsky

March 27-29, 2006
Coxeter Lecture Series -- Yair Minsky (Yale)

May 15-19, 2006
Mini-course on Recent advances in hyperbolic 3-manifolds
Jeff Brock (Brown University)
Ken Bromberg (University of Utah)
Dick Canary (University of Michigan)
Juan Souto (University of Chicago)

May 23-27, 2006
Hyperbolic geometry Workshop
Org. Cttee: Y. Minsky, B. Kleiner

Fall 2005
Thematic Program on Renormalization and Universality in Mathematics and Mathematical Physics

Pavel Bleher (IUPUI)
Mikhail Lyubich (Toronto,SUNY Stony Brook)
Michael Yampolsky (Toronto)

Scientific Committee:

Edouard Brezin (École Normale, Paris)
Giovanni Gallavotti (University of Rome)
Leo Kadanoff (University of Chicago)
Dirk Kreimer (IHÉS & Boston University)
Oscar Lanford (ETH Zurich)
Robert MacKay (Warwick)

David Ruelle (IHÉS)
Michael Sigal (University of Toronto)
Yakov Sinai (Princeton)
Thomas Spencer (IAS)
Dennis Sullivan (CUNY & SUNY Stony Brook)
Jean-Bernard Zuber (Saclay)

Overview of the program

The program will aim to give a broad prospective of application of renormalization ideas. The concentration will be in the areas where renormalization and scaling invariance led to important recent progress, such as one-dimensional dynamics (real and complex), 2D conformal invariance, geometric PDEs, and their connection to the underlying physics ideas. The purpose is two-fold: to survey the recent achievements and outline new directions of research on the one hand; and to foster the interaction between various branches of the dynamics and mathematical physics communities working in renormalization.

The first half of the program will concentrate on the physical aspects of renormalization: statistical physics, conformal field theory, the underlying Hopf-algebraic structure, renormalization in PDE. The second half will have the dynamical flavour: holomorphic and smooth dynamics; KAM theory and renormalization of Hamiltonian flows; conformal invariance and universality in 2D stochastic processes. We also plan to touch on the recent breakthrough in the Geometrization Program based on the dynamics of the Ricci Flow and its connection to the concept of renormalization. The program will include two workshops: one in September-October, focused on mathematical physics, and one in December, focused on Dynamics. There will be a series of graduate courses and mini-courses on topics including:

  • Renormalization in one-dimensional dynamics;
  • Renormalization in infinite-dimensional dynamical systems;
  • Renormalization in mathematical physics;
  • Renormalization in Hamiltonian systems;
  • Hopf-algebraic aspects of renormalization;
  • Percolation, Brownian motion, and SLE.

Fall 2005 Workshops

Dynamical Systems Seminar
Mondays, 3:10 p.m. - Room 230

Mini Courses
Tuesdays & Thursdays, 1:10 p.m., Wednesdays, 2:10 p.m. - Library

Computability and Complexity in Analysis and Dynamics Seminar
Fridays, 2:10 p.m. - Bahen Bldg., BA 3004

September 13-15, 2005
Coxeter Lecture Series -- Oded Schramm, Microsoft

September 20-24, 2005
Percolation, SLE, and related topics Workshop
Organizing Committee: Ilia Binder (Toronto), Steffen Rohde (University of Washington)

October 18-22, 2005
Renormalization and universality in mathematical physics Workshop
Organizing Committee: Pavel Bleher (IUPUI) , Dirk Kreimer (CNRS-IHES & Boston University)

October 24, 2005
Clay Math Institute Public Lecture -- Leo Kadanoff, UChicago

Nov 23-25, 2005
Coxeter Lecture Series
Lai-Sang Young, Courant Institute of Mathematical Sciences

November 29 - December 3, 2005
Renormalization in dynamical systems Workshop
Organizing Committee: Hans Koch (Texas) , Misha Lyubich (Toronto), Michael Yampolsky (Toronto)
Register to attend

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