THEMATIC PROGRAMS

Thematic Program on the Foundations of Computational Mathematics July-December, 2009

November 16 - 21, 2009
Workshop on Computational Differential Geometry, Topology, and Dynamics

Organizing Committee:
Richard Schwartz (Brown University)- Chair
Alex Nabutovsky (University of Toronto)
Carles Simo (University of Barcelona)
Michael Yampolsky (University of Toronto)

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Audio and slides of talks

Workshop Overview

This workshop will deal with the interaction between computation and topics in geometry, topology, and dynamics. Topics include, among other things, recognition problems in geometry and topology, the computation of geometric structures on topological spaces, undecidability results in geometry and topology, algorithms for drawing dynamically interesting sets in the plane, algorithmic aspects of geometric group theory, computational properties in convex geometry, computer-aided proofs of dynamical behavior, numeric/symbolic algorithms and the corresponding computer to obtain invariant manifolds, homoclinic phenomena, etc in non-rigorous and rigorous implementations, and computer exploration of dynamical systems aiming at describing global properties of the dynamics and suggesting theoretical results. Complexity of these algorithms will also be discussed.

Invited Speakers

Zin Arai (Hokkaido) Dror Bar-Natan (Toronto) Carlos Beltran (Cantabria) Martin Berz (Michigan State) Ilia Binder (Toronto) Mark Braverman (Microsoft Research) Nathan Dunfield (Illinois) Herbert Edelsbrunner (Duke) Joel Hass (UC, Davis) Pat Hooper (Northwestern) Angel Jorba (University of Barcelona)* Svetlana Katok (Pennsylvania State) Stefano Luzzatto (ICTP) Assaf Naor (NYU )* Sheldon Newhouse (Michigan State)

Igor Pak (UCLA) Roland Roeder (SUNY Stony Brook) Saul Schleimer (Warwick) Richard Schwartz (Brown) Carles Simó (Universidad de Barcelona) Sergei Tabachnikov (Pennsylvania State) Morwen Thistlethwaite (Tennessee) Dylan Thurston (Barnard College,Columbia ) Warwick Tucker (Uppsala ) Shmuel Weinberger (Chicago) Daniel Wilczak (Bergen) Yosef Yomdin (Weizmann Institute) Piotr Zgliczynski (Jagiellonian) * may be confirmed

Workshop Schedule

Monday November 16, 2009
8:45-9:00 am	Welcome and Introduction Fields Director and Workshop Organizers
9:00-10:00	Shmuel Weinberger (Chicago) Persistent homology of data, loop spaces, and landscapes
10:00-11:00	Herbert Edelsbrunner (Duke University) Measuring with algebra
11:00-1:00 pm	Lunch Break
1:00-2:00	Svetlana Katok (Pennsylvania State University) Reduction theory and coding of geodesics on the modular surface
2:00-3:00	Piotr Zgliczynski (Jagiellonian University) Heteroclinic connections between fixed points for Kuramoto-Sivashinki PDE, a computer assisted proof
3:00-4:00	Break
4:00-5:00	Ilia Binder (Toronto) Walk on Sphere algorithm and boundary geometry
5:00-6:00	Reception Fields Atrium
Tuesday November 17, 2009
9:00-10:00am	Morwen Thistlethwaite (Tennessee) The exact computation of some representation varieties
10:00-11:00	Warwick Tucker (Uppsala) A rigorous lower bound for the stability regions of the quadratic map
11:00-1:00	Lunch Break
1:00- 2:00	Yosef Yomdin (The Weizmann Institute of Science) I. Center-Focus Problem for Abel equation, Moment vanishing, Compositions, and Mathieu and Zhao conjectures
2:00-3:00	Igor Pak (UCLA) Acute triangulations of polytopes
3:00-4:00	Break
4:00-5:00	Sergei Tabachnikov (Penn State University) Pentagrama Myrificum, Old wine into new wineskins
Wednesday November 18, 2009
9:00-10:00	Dylan Thurston (Barnard College, Columbia) Rigidity of Graphs
10:00-11:00	Roland Roeder (SUNY Stony Brook) Computing arithmetic invariants for hyperbolic reflection groups
11:00-1:00	Break
1:00-2:00	Stefano Luzzatto (International Centre for Theoretical Physics, ICTP) Deciding the undecidable: Probabilistic arguments versus finite resolution dynamics
2:00-3:00	Carles Simó (Universidad de Barcelona) The role of Dynamical Systems in Celestial Mechanics.Applications to Astronomy and Astrodynamics
Thursday November 19, 2009
9:00-10:00	Zin Arai (Hokkaido University) Rigorous verification of uniform hyperbolicity, subshifts of finite type and the pruning front
10:00-11:00	Carlos Beltran (Universidad de Cantabria) A difficult minimization problem: the distribution of points in the sphere
11:00-1:00	Lunch Break
1:00-2:00	Joel Hass (University of California, Davis) Unknot diagrams requiring a quadratic number of Reidemeister moves to untangle
2:00-3:00	Yosef Yomdin (The Weizmann Institute of Science) II. "Algebraic" reconstruction of Signals and Images from Fourier Data
3:00-4:00	Break
4:00-5:00	Pat Hooper (Northwestern University) Billiards in nearly isosceles triangles
Friday November 20, 2009
9:00-10:00	Daniel Wilczak (University of Bergen) Rigorous numerics for homoclinic tangencies
10:00-11:00	Saul Schleimer (University of Warwick) Twister: building triangulations of surface bundles
11:00 - 1:00	Break
1:00 - 2:00	Richard Schwartz (Brown University) Polygonal Outer Billiards
2:00-3:00	Nathan Dunfield (Illinois) Practical solutions to hard problems in 3-dimensional topology
3:00-3:30	Break
3:30-4:30	Martin Berz (Michigan State) tba
Saturday November 21, 2009
10:00-11:00	Mark Braverman (Microsoft Research) Computability and Complexity of Julia Sets
11:00-12:00	Dror Bar-Natan (Toronto) Dessert: Hilbert's 13th Problem, in Full Colour

 

Confirmed Participants as of November 24, 2009

Full Name	University/Affiliation
Amelunxen, Dennis	Universität Paderborn
Andrews, Rob	(no affiliation)
Arai, Zin	Hokkaido University
Armentano, Diego	Universidad de la República
Bar-Natan, Dror	University of Toronto
Beltrán, Carlos	Universidad de Cantabria
Berz, Martin	Michigan State University
Binder, Ilia	University of Toronto
Braverman, Mark	Microsoft Research
Briquel, Irénée	Ecole Normale Supérieure de Lyon
Conidis, Chris	University of Waterloo
Coons, Michael J.	Simon Fraser University
Cucker, Felipe	City University of Hong Kong
Dedieu, Jean-Pierre	Université de Toulouse
Dunfield, Nathan	University of Illinois at Urbana-Champaign
Edelsbrunner, Herbert	IST Austria
Franklin, Johanna	National University of Singapore
Fraser, Maia	University of Chicago
Grenet, Bruno	Ecole Normale Supérieure de Lyon
Grigo, Alexander	Georgia Institute of Technology
Ha Quang, Minh	Humboldt University
Halevy, Itamar
Hammerlindl, Andy	The Fields Institute
Hass, Joel	University of California, Davis
Hauenstein, Jonathan	University of Notre Dame
Hooper, Patrick	Northwestern University
Hooper, William	Northwestern University
Huerfano, Stella	National University of Colombia
Johnson, Tomas	Uppsala University
Katok, Svetlana	Pennsylvania State University
Kenny, Robert	University of Western Australia
Khanin, Konstantin	University of Toronto
Kim, Andrew	University of Toronto
Koiran, Pascal	ENS Lyon
Krick, Teresa	Universidad de Buenos Aires
Li, Tien-Yien	Michigan State University
Luzzatto, Stefano	International Centre for Theoretical Physics (ICTP)
Makino, Kyoko	Michigan State University
Nabutovsky, Alexander	University of Toronto
Newhouse, Sheldon	Michigan State University
Nobakhtian, Soghra	University of Isfahan
Pak, Igor	University of California, Los Angeles
Pang, Chin How Jeffrey	Cornell University
Parlier, Hugo	University of Toronto
Portier, Natacha	ENS Lyon
Rej, Abhijnan	Fields Institute
Renegar, James	Cornell University
Roeder, Roland	SUNY Stony Brook
Rojas, Cristóbal	IML
Sadri, Bardia	University of Toronto
Schleimer, Saul	University of Warwick
Schwartz, Richard	Brown University
Sethuraman, Swaminathan	Fields Institute
Shub, Michael	University of Toronto
Simó, Carles	Universidad de Barcelona
Sudarsandhari Shibani, Wilson	EPFL
Tabachnikov, Sergei	Penn State University
Tan, Ser Peow	National University of Singapore
Thistlethwaite, Morwen	University of Tennessee
Thurston, Dylan	Barnard College, Columbia University
Todd, Michael J.	Cornell University
Tucker, Warwick	Uppsala University
Ulgen Yildirim, Semail	Northwestern University
Weinberger, Shmuel	University of Chicago
Wilczak, Daniel	Jagiellonian University and Uppsala Universitet
Wittig, Alexander	Michigan State University
Yampolsky, Michael	University of Toronto
Yomdin, Yosef	The Weizmann Institute of Science
Young, Robert	Institut des Hautes Etudes Scientifiques
Zgliczynski, Piotr	Jagiellonian University
Zuev, Konstantin	Lomonosov Moscow State University

Apply to the Program:
All scientific events are open to the mathematical sciences community. Visitors who are interested in office space or funding are requested to apply by filling out the application form. Additional support is available (pending NSF funding) to support junior US visitors to this program. Fields scientific programs are devoted to research in the mathematical sciences, and enhanced graduate and post-doctoral training opportunities. Part of the mandate of the Institute is to broaden and enlarge the community, and to encourage the participation of women and members of visible minority groups in our scientific programs.

For additional information contact thematic(PUT_AT_SIGN_HERE)fields.utoronto.ca

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