April 22, 2024
Thematic Program on Asymptotic Geometric Analysis July - December 2010

November 1-5, 2010
Workshop on Geometric Probability and Optimal Transportation

Organizers: B. Klartag and R. McCann

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October 25-29, 2010 Concentration period on Partial Differential Equations and Geometric Analysis
November 1-5, 2010 Workshop on Geometric Probability and Optimal Transportation
November 8, 2010 Concentration period on Nonlinear Dynamics and Applications

The Nov 1-5 Workshop is devoted to the investigation of geometric and probablistic questions through the use of optimal transportation. Topics to be addressed include convex geometry, inequalities and isoperimetry, notions of curvature (sectional, Ricci, and scalar) in metric-measure spaces, high dimensional limits, geometrization of the space of probability measures, and dynamics thereon --- dissipative and conservative, classical, fluid, quantum, and geometrical flows.

The Workshop will be preceded by a week devoted to partial differential equations and geometric analysis (Oct 25-29), focused especially on recent developments concerning regularity of optimal maps, the infinity Laplacian, mean-field games, fully nonlinear degenerate elliptic equations of Monge-Ampere type, and design problems from engineering to economics. The workshop will be followed by several days devoted to nonlinear dynamics and applications (Nov 8-10), including pattern formation, diffusive dynamics, kinetic theory, solid, fluid and wave mechanics, and the weak KAM theory.


If you are willing to give a talk during the Workshop or its adjacent concentration periods "Partial Differential Equations and Geometric Analysis" ( Oct 25-29) and "Nonlinear Dynamics and Applications" (Nov 8), please suggest a title and abstract. Note that although not all participants will be able to speak, all submitted abstracts will be compiled and distributed, to facilitate the exchange of ideas. Time will also be allocated to short communications and to poster presentations.


Schedule (talk titles and abstracts)

Monday October 25 - 3rd Floor Stewart Library
2:00 - 2:10 Welcome and Introduction
Fields Director Ed Bierstone and Workshop Organizers
2:10 - 3:00 Frank Morgan (Williams College)
Densities from Geometry to Poincaré
3:05 - 4:10 Coffee Break
4:10 - 5:00 Israel Michael Sigal (University of Toronto)
Singularity formation under the mean-curvature flow
5:00 - 6:30 Reception - cash bar
Fields Institute Atrium
Tuesday October 26 - Room 230
10:00 - 10:50 Aldo Pratelli (Pavia (Italy))
About the approximation of orientation-preserving homeomorphisms via piecewise affine or smooth ones
10:55 - 11:10 Coffee Break
11:10 - 12:00 Mariya Shcherbina (Institute for Low Temperature Physics Ukr. Ac. Sci)
Orthogonal and symplectic matrix models: universality and other properties
12:05 - 2:10 Lunch Break
2:10 - 3:00 Graduate Minicourse (part 1)- Scott Armstrong (University of Chicago)
An introduction to infinity harmonic functions
3:10 - 4:00 Graduate Minicourse (part 2)- Charles Smart (New York University)
An introduction to infinity harmonic functions
Wednesday October 27 - Room 230
10:00 - 10:50 Tony Gomis (NBI)
A domian Decomposition Method, Cherruault Transformations, Homotopy Perturbation Method, and Nonlinear Dynamics: Theories and Comparative Applications to Frontier problems
10:55 - 11:10 Coffee Break
11:10 - 12:00 Jerome Bertrand (University Paul Sabatier Toulouse)
Wasserstein space over Hadamard space
12:05 - 2:10 Lunch Break
2:10 - 2:35 Amir Moradifam (University of Toronto)
Isolated Singularities of Polyharmonic Inequalities
2:40 - 3:05 Magda Czubak (University of Toronto)
Topological defects in the abelian Higgs model
3:10 - 4:00 Coffee Break
4:10 - 5:00 (F Morgan Math Dept Colloquium in BA 6183)
Thursday October 28 - Stewart Library
10:10 - 11:00 Graduate Minicourse (part 3)- Scott Armstrong (University of Chicago)
An introduction to infinity harmonic functions
11:10 - 12:00 Graduate Minicourse (part 4)- Charles Smart (New York University)
An introduction to infinity harmonic functions
12:10 - 1:00 Jiakun Liu (Princeton University) - Room 210
Global regularity of the reflector problem
  Free Afternoon
Friday October 29 - Room 210
10:55 - 11:10 Coffee Break
11:10 - 12:00 Philippe Delanoe (CNRS at University of Nice Sophia Antipolis)
Remarks on the regularity of optimal transport
12:10 - 1:00 Young-Heon Kim (University of British Columbia)
Regularity of optimal transport maps on multiple products of spheres
1:05 - 2:10 Lunch Break
2:10 - 3:00 Off-site (Holzegel Math Dept seminar in BA 6183)
3:00 - 3:30 Fields Coffee Break
Monday November 1 - Room 230
10:00 - 10:50 Alexander Plakhov (University of Aveiro)
Optimal mass transportation and billiard scattering by rough bodies
10:55 - 11:10 Coffee Break
11:10 - 12:00 Brendan Pass (University of Toronto)
The multi-marginal optimal transportation problem
12:05 - 2:10 Lunch Break
2:10 - 2:35 Alexander Kolesnikov (MSUPA and HSE (Moscow))
Sobolev regularity of optimal transportation
2:40 - 3:05 Gabriel Maresch (TU Vienna)
Optimal and Better Transport Plans
3:10 - 3:40 Coffee Break
3:40 - 4:05 Emil Saucan (Department of Mathematics, Technion, Haifa, Israel)
Triangulation and discretizations of metric measure spaces
4:10 - 4:35 Jun Kitagawa (Princeton University)
Regularity for the optimal transport problem with Euclidean distance squared cost on the embedded sphere
5:00 - 6:00 Cédric Villani (Institut Henri Poincaré, Université Claude Bernard Lyon 1) - in Bahen 1160
What is the fate of the solar system?

(**Note registration is required as space is limited)
Tuesday November 2 - Room 230
10:00 - 10:50 Nassif Ghoussoub (University of British Columbia)
Homogenization, inverse problems and optimal control via selfdual variational calculus
10:55 - 11:10 Coffee Break
11:10 - 12:00 Yi Wang (Princeton University)
The Aleksandrov-Fenchel inequalities of k+1-convex domains
12:05 - 2:10 Lunch Break
2:10 - 4:00 Graduate Minicourse -Vitali Milman (Tel Aviv University)
Overview of Asymptotic Geometric Analysis; an Introduction
4:10 - 5:00 Alexander Koldobsky (University of Missouri-Columbia)
Positive definite functions and stable random vectors
5:10 - 6:00 Nicola Gigli (University of Nice) *note this talk will be held in the 3rd floor Stewart Library*
The Heat Flow as Gradient Flow
Wednesday November 3 - Room 230
10:00 - 10:50 Irene M. Gamba (The University of Texas at Austin)
Convolution inequalities for Boltzmann collision operators and applications
10:55 - 11:10 Coffee Break
11:10 - 12:00 Micah Warren (Princeton University)
Parabolic optimal transport equations on compact manifolds
12:05 - 2:10 Lunch Break
2:10 - 3:00 Dmitry Jakobson (McGill University, Department of Mathematics and Statistics)
Curvature of Random Metrics
3:05 - 3:30 Alfredo Hubard (NYU)
Can you cut a convex body into five convex bodies, with equal areas and equal perimeters?
3:30 - 3:55 Coffee Break
4:00 - 5:00 Cedric Villani (l'Institut Henri Poincaré, Université Claude Bernard Lyon 1)
Particle systems and Landau damping
5:00- 6:30 Reception
Thursday November 4 - Room 230
10:10 - 11:00 Graduate Course - Alessio Figalli (University of Texas at Austin)
The geometry of the Ma-Trudinger-Wang condition
11:10 - 12:00 Cedric Villani (l'Institut Henri Poincaré, Université Claude Bernard Lyon 1)
From echo analysis to nonlinear Landau damping
12:05 - 2:10 Lunch Break
2:10 - 2:35 Michael Loss (School of Mathematics, Georgia Tech)
Hardy-Littlewood-Sobolev Inequalities via Fast Diffusion Flows
2:40 - 3:05 Mark Meckes (Case Western Reserve University)
The magnitude of a metric space
3:10 - 3:40 Coffee Break
3:40 - 4:05 Shaghayegh Kordnoori (Islamic Azad University North Tehran Branch)
Central Limit Theorem and geometric probability
4:10 - 4:35 Marjolaine Puel (IMT Toulouse, France)
Jordan-Kinderlehrer-Otto scheme for a relativistic cost
4:40 - 5:30 Joseph Lehec (Universit Paris-Dauphine)
A stochastic formula for the entropy and applications
Friday November 5 - Room 230
10:00 - 10:50 Luigi Ambrosio (Scuola Normale Superiore)
Elements of Geometric Measure Theory in Wiener spaces
10:55 - 11:10 Coffee Break
11:10 - 12:00 Paul Woon Yin Lee (UC Berkeley)
Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian Manifolds
12:05 - 2:10 Lunch
2:10 - 3:00 Elton Hsu (Department of Mathematics, Northwestern University)
Mass Transportation and Optimal Coupling of Brownian Motions
3:05 - 3:35 Coffee Break
3:40 - 4:30 Emanuel Milman (University of Toronto)
A generalization of Caffarelli's Contraction Theorem via heat-flow
4:40 - 5:30 Wilfrid Gangbo (Georgia Institute of Technology)
Sticky Particle Dynamics with Interactions
Monday November 8 - Room 230
10:00 - 10:50 Konstantin Khanin (University of Toronto)
Lagrangian dynamics on shock manifolds
10:55 - 11:10 Coffee Break
11:10 - 12:00 Walter Craig (Department of Mathematics & Statistics, McMaster University)
On the size of the Navier - Stokes singular set
12:05 - 2:10 Lunch Break
2:10 - 3:00 Marina Chugunova (University of Toronto)
Finite speed propagation of the interface and blow-up solutions for long-wave unstable thin-film equations
3:05 - 3:30 Coffee Break
3:30 - 4:20 Gideon Simpson (University of Toronto)
Coherent Structures in the Nonlinear Maxwell Equations
4:30 - 5:20 Stephen W. Morris (University of Toronto)
Icicles, washboard road and meandering syrup
5:30 - 6:30 Poster session/ Small Reception
Wednesday November 10
Joint Concentration Period on Nonlinear Dynamics and Applications and Colloquium in Applied Mathematics
2:10 - 3:00 Boris Khesin (University of Toronto)
Optimal transport and geodesics for H^1 metrics on diffeomorphism groups

Confirmed Participants

Fullname University/Affiliation
Adamczak, Radosaw University of Warsaw
Alonso-Gutiérrez, David University of Zaragoza
Ambrosio, Luigi Scuola Normale Superiore
Armstrong, Scott University of Chicago
Badali, Daniel University of Toronto
Bartosova, Dana University of Toronto
Bertrand, Jérôme Université Paul Sabatier
Bezuglyi, Sergei B.Verkin Institute for Low Temperature Physics and Engineering
Bikila, Dejene Woldesemayat Hasselt University
Chen, Shibing University of Toronto
Choksi, Rustum McGill University
Chugunova, Marina University of Toronto
Colesanti, Andrea Università degli Studi di Firenze
Coskey, Sam The Fields Institute
Craig, Walter McMaster University
Czubak, Magdalena University of Toronto
Dafni, Galia Concordia University
Dafnis, Nikolaos University of Athens
Dann, Susanna Louisiana State University
De Queiroz, Olivaine Princeton University
Delanoë, Philippe CNRS, University of Nice
Dotterrer, Dominic University of Toronto
Ellis, Paul University of Connecticut
Faifman, Dmitry Tel Aviv University
Fernández-Unzueta, Maite CIMAT
Figalli, Alessio The University of Texas at Austin
Funano, Kei Kumamoto University
Gamba, Irene M. University of Texas
Gangbo, Wilfrid Georgia Institute of Technology
Ghoussoub, Nassif University of British Columbia
Gigli, Nicola University of Bonn
Ginsberg, Dan University of Toronto
Gomis, Tony NBI-France
Guédon, Olivier Université Paris-Est Marne La Vallée
Guth, Larry University of Toronto
Gutman, Yonatan Université Paris-Est Marne-la-Vallée
Holland, James Australian National University
Hsu, Elton Northwestern University
Hubard, Alfred CIMS of NYU
Hug, Daniel Universität Karlsruhe (TH)
Illner, Reinhard University of Victoria
Jakobson, Dmitry McGill University
Jiménez, Carlos Hugo University of Seville
Khesin, Boris University of Toronto
Kim, Hyojin  
Kim, Young-Heon University of British Columbia
Kislyakov, Sergei St.Petersburg Department of Steklov Institute of Mathematics
Kitagawa, Jun Princeton University
Klartag, Boaz Tel-Aviv University
Koldobsky, Alexander University of Missouri
Kolesnikov, Alexander MSUPA
Kordnoori, Shaghayegh Azad University North Tehran Branch
Kwiatkowska, Aleksandra University of Illinois at Urbana-Champaign
Labibi, Batool University of Toronto
Latala, Rafal University of Warsaw
Lee, Woon Yin (Paul) University of California, Berkeley
Litvak, Alexander University of Alberta
Liu, Jiakun Princeton University
López-Abad, Jorge Instituto de Ciencias Matemáticas
Loss, Michael Georgia Institute of Technology
Maresch, Gabriel TU Vienna
McCann, Robert University of Toronto
Meckes, Mark Case Western Reserve University
Melleray, Julien Université Lyon 1
Mérigot, Quentin The Fields Institute
Milman, Emanuel University of Toronto
Milman, Vitali Tel Aviv University
Moradifam, Amir University of Toronto
Morgan, Frank Williams College
Morris, Stephen W. University of Toronto
Nguyen Van Thé, Lionel Université Paul Cézanne - Aix-Marseille III
Osadolor, Anthony Technical University, Hamburg
Paouris, Grigoris Texas A&M University
Pass, Brendan University of Toronto
Pastur, Leonid National Academy of Sciences of Ukraine
Pestov, Vladimir University of Ottawa
Pivovarov, Peter University of Alberta
Plakhov, Alexander University of Aveiro
Pratelli, Aldo Università di Pavia
Puel, Marjolaine Université Paul Sabatier
Rahbarnia, Freydoon Ferdowsi University
Rahman, Mustazee University of Toronto
Reitzner, Matthias University of Osnabrueck
Rotem, Liran Tel Aviv University
Saucan, Emil Technion
Sauer, Norbert University of Calgary
Savaré, Giuseppe University of Pavia
Schechtman, Gideon Weizmann Institute of Science
Schuster, Franz Vienna University of Technology
Segal, Alexander Tel Aviv University
Shcherbina, Mariya National Academy of Sciences of Ukraine
Sigal, Israel Michael University of Toronto
Simpson, Gideon University of Toronto
Slomka, Boaz Tel Aviv University
Slutsky, Konstantin University of Illinois at Urbana-Champaign
Smart, Charles Courant Institute of Mathematical Sciences
Spektor, Susanna University of Alberta
Stancu, Alina Concordia University
Taschuk, Steven University of Alberta
Tiglay, Feride The Fields Institute
Tomczak-Jaegermann, Nicole University of Alberta
Tsankov, Todor Université Paris Diderot-Paris 7
Valettas, Peter University of Athens
Wang, Yi Princeton University
Warren, Micah Princeton University
Wolff, Pawel University of Warsaw
Ye, Deping Fields Institute
Zouzias, Anastasios University of Toronto


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