
THEMATIC PROGRAMS 

June 30, 2016  
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Spring 2006


Mike Shub (Toronto) Michael Yampolsky (Toronto) 
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) 
The main focus of this program will be on the interaction between 3dimensional 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 twodimensional 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 minicourses on the topics of the program.
Dynamical Systems Seminar
Mondays, 3:10 p.m.  Room 230Mini Courses
Wednesdays, 1:30 p.m., Fridays, 1:30 p.m.(if needed)  Room 230Computability and Complexity in Analysis and Dynamics Seminar
Fridays, 2:10 p.m.  Bahen Bldg., BA 026Young People Dynamics Seminar
Friday at 5pm, Fields LibraryJanuary 59, 2006
Partially hyperbolic dynamics, laminations, and Teichmuller flow Workshop
Org. Cttee: G. Forni, M. Lyubich, C. Pugh, M. Shub
Jan 91011, 2006
Distinguished Lectures by Gregory MargulisMarch 711, 2006
Holomorphic dynamics Workshop
In celebration of John Milnor's 75th birthday
Org. Cttee: M. Lyubich, J. Smillie, M. Yampolsky
March 2729, 2006
Coxeter Lecture Series  Yair Minsky (Yale)
May 1519, 2006
Minicourse on Recent advances in hyperbolic 3manifolds
Jeff Brock (Brown University)
Ken Bromberg (University of Utah)
Dick Canary (University of Michigan)
Juan Souto (University of Chicago)May 2327, 2006
Hyperbolic geometry Workshop
Org. Cttee: Y. Minsky, B. Kleiner

David Ruelle (IHÉS) Michael Sigal (University of Toronto) Yakov Sinai (Princeton) Thomas Spencer (IAS) Dennis Sullivan (CUNY & SUNY Stony Brook) JeanBernard Zuber (Saclay) 
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 onedimensional dynamics (real and complex), 2D conformal invariance,
geometric PDEs, and their connection to the underlying physics ideas.
The purpose is twofold: 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 Hopfalgebraic 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 SeptemberOctober, focused on mathematical physics, and one in December, focused on Dynamics. There will be a series of graduate courses and minicourses on topics including:
 Renormalization in onedimensional dynamics;
 Renormalization in infinitedimensional dynamical systems;
 Renormalization in mathematical physics;
 Renormalization in Hamiltonian systems;
 Hopfalgebraic aspects of renormalization;
 Percolation, Brownian motion, and SLE.
Fall 2005 Workshops
Dynamical Systems Seminar
Mondays, 3:10 p.m.  Room 230Mini Courses
Tuesdays & Thursdays, 1:10 p.m., Wednesdays, 2:10 p.m.  LibraryComputability and Complexity in Analysis and Dynamics Seminar
Fridays, 2:10 p.m.  Bahen Bldg., BA 3004September 1315, 2005
Coxeter Lecture Series  Oded Schramm, Microsoft
September 2024, 2005
Percolation, SLE, and related topics Workshop
Organizing Committee: Ilia Binder (Toronto), Steffen Rohde (University of Washington)
October 1822, 2005
Renormalization and universality in mathematical physics Workshop
Organizing Committee: Pavel Bleher (IUPUI) , Dirk Kreimer (CNRSIHES & Boston University)
October 24, 2005
Clay Math Institute Public Lecture  Leo Kadanoff, UChicagoNov 2325, 2005
Coxeter Lecture Series
LaiSang Young, Courant Institute of Mathematical SciencesNovember 29  December 3, 2005
Renormalization in dynamical systems Workshop
Organizing Committee: Hans Koch (Texas) , Misha Lyubich (Toronto), Michael Yampolsky (Toronto)
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Contact: holodynamics@fields.utoronto.ca