December  9, 2023

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)
Saturday November 21, 2009
10:00-11:00 Mark Braverman (Microsoft Research)
Computability and Complexity of Julia Sets

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

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