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MSRI Summer Microprogram on Nonlinear Partial Differential Equations
Jul 23, 2007
to
Aug 10, 2007
Organizer(s)
L. C. Evans (UC Berkeley, Chair), C. Gutierrez (Temple), C. Sogge (Johns Hopkins), D. Tataru (UC Berkeley)
To apply for funding, you must
register by Mon, Jun 04 2007.
This three week program will emphasize the overlapping research areas of nonlinear dispersive equations (NDE) and nonlinear elliptic equations (NEE), and is intended as an extension of the MSRI programs in these fields from Fall, 2005, with a focus on subsequent research developments. Weeks 1 and 3 will comprise informal but focused workshops on NEE and NDE, respectively. Topics of emphasis will include regularity estimates for elliptic PDE, with applications to mass transport problems and to image processing. The NDE workshop will focus upon eigenfunction estimates, resonances and spectral resolutions for elliptic operators on manifolds. Week 2 will be devoted to several expository minicourses, of general interest, especially for younger mathematicians. We are currently planning these lecture series: - Craig Evans, "Survey of weak convergence methods for nonlinear PDE'"
- Cristian Gutierrez, "The Monge-Ampere equation''
- Chris Sogge, "Dispersion and existence theorems for nonlinear wave equations"
- Daniel Tataru, "Nonlinear wave equations''
A block of rooms has been reserved at the Hotel Durant. Please mention the workshop name and reference the following code when making reservations via phone, fax or e-mail: TQ0000. The cut-off date for reservations is Jun 22, 2007.
Funding
Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are made typically 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.
| Schedule |
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| Monday, July 23, 2007 |
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1:00PM - 1:50PM |
Panagiotis Souganidis
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Error estimates for approximations to viscosity solutions of uniformly elliptic second-order pde
[Video available]
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2:00PM - 2:50PM |
Hongjie Dong
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On the Green's matrices of strongly elliptic and parabolic systems of second order
[Video available]
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4:00PM - 4:50PM |
Russell Schwab
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Stationary Ergodic Homogenization of Time Dependent Hamliton-Jacobi
[Video available]
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| Tuesday, July 24, 2007 |
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1:00PM - 1:50PM |
Young-Heon Kim
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Curvature and the continuity of optimal transportation maps
[Video available]
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2:00PM - 2:50PM |
Maria Gonzalez
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Fractional powers of the Laplacian and some applications
[Video available]
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4:00PM - 4:50PM |
Luigi De Pascale
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Local solutions and existence of optimal transport maps for the $$W_\infty$$ Wasserstein distance. Extensions to more classical Monge problems.
[Video available]
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| Wednesday, July 25, 2007 |
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1:00PM - 1:50PM |
Robert Jensen
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Super- and sub-solutions of Aronsson equations
[Video available]
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2:00PM - 2:50PM |
Yifeng Yu
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Asymptotic behaviour of infinity harmonic functions near isolated singularities.
[Video available]
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4:00PM - 4:50PM |
Sun-Sig Byun
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Hessian Estimates for fourth order parabolic equations
[Video available]
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| Thursday, July 26, 2007 |
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1:00PM - 1:50PM |
Cristian Gutierrez
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The refractor problem in reshaping light beams
[Video available]
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2:00PM - 2:50PM |
Craig Evans
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More PDE methods for weak KAM theory
[Video available]
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| Monday, July 30, 2007 |
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9:00AM - 9:45AM |
Christopher Sogge
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Dispersion, Nonlinear Wave Equations 1
[Video available]
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10:00AM - 10:45AM |
Cristian Gutierrez
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The Monge-Ampere Equation 1
[Video available]
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11:00AM - 11:45AM |
Christopher Sogge
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Dispersion, Nonlinear Wave Equations 2
[Video available]
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12:00PM - 12:45PM |
Cristian Gutierrez
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The Monge-Ampere Equation 2
[Video available]
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| Tuesday, July 31, 2007 |
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9:00AM - 9:50AM |
Christopher Sogge
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Dispersion, Nonlinear Wave Equations 3
[Video available]
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10:30AM - 11:20AM |
Cristian Gutierrez
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The Monge-Ampere Equation 3
[Video available]
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11:40AM - 12:30PM |
Christopher Sogge
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Dispersion, Nonlinear Wave Equations 4
[Video available]
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| Wednesday, August 01, 2007 |
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9:00AM - 9:50AM |
Cristian Gutierrez
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The Monge-Ampere Equation 4
[Video available]
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10:30AM - 11:20AM |
Daniel Tataru
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Nonlinear Wave Equations 1
[Video available]
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11:40AM - 12:30PM |
Craig Evans
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Weak Convergence Methods 1
[Video available]
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| Thursday, August 02, 2007 |
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9:00AM - 9:50AM |
Daniel Tataru
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Nonlinear Wave Equations 2
[Video available]
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10:30AM - 11:20AM |
Craig Evans
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Weak Convergence Methods 2
[Video available]
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11:40AM - 12:30PM |
Daniel Tataru
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Nonlinear Wave Equations 3
[Video available]
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| Friday, August 03, 2007 |
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9:00AM - 9:50AM |
Craig Evans
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Weak Convergence Methods 3
[Video available]
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10:30AM - 11:20AM |
Daniel Tataru
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Nonlinear Wave Equations 4
[Video available]
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11:40AM - 12:30PM |
Craig Evans
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Weak Convergence Methods 4
[Video available]
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| Monday, August 06, 2007 |
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9:00AM - 10:00AM |
Michael Christ
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Christ-1
[Video available]
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2:00PM - 3:00PM |
Herbert Koch
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Koch-1
[Video available]
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4:00PM - 5:00PM |
Slim Ibrahim
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Around the 2D Energy of NLKG
[Video available]
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| Tuesday, August 07, 2007 |
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9:00AM - 10:00AM |
Justin Holmer
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Holmer-1
[Video available]
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11:00AM - 12:00PM |
Robert McCann
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McCann-1
[Video available]
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11:00AM - 12:00PM |
Jason Metcalfe
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Global-in-time Strichartz estimates for asymptotically flat Schr\"odinger equations
[Video available]
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2:00PM - 3:00PM |
Hart Smith
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Lp Bounds on Eigenfunctions for Lipschitz Metrics
[Video available]
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4:00PM - 5:00PM |
Dan Geba
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Quadratic Linear Wave Equations
[Video available]
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| Wednesday, August 08, 2007 |
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9:00AM - 10:00AM |
Jacob Sterbenz
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Sterbenz-1
[Video available]
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10:00AM - 11:00AM |
Neil Trudinger
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Tradinger-1
[Video available]
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11:00AM - 12:00PM |
Ioan Bejenaru
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Global solutions for Schroedinger Maps
[Video available]
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| Thursday, August 09, 2007 |
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9:00AM - 10:00AM |
Maciej Zworski
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Local Smoothing in the Presence of Lots of Trapping
[Video available]
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10:00AM - 11:00AM |
Szu-yu Sophie Chen
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S. Chen-1
[Video available]
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11:00AM - 12:00PM |
Becca Thomases
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Thomases-1
[Video available]
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2:00PM - 3:00PM |
Matthew Blair
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Strichartz Estimates on Manifolds with Boundary
[Video available]
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4:00PM - 5:00PM |
Jeremy Marzuola
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Marzuola-1
[Video available]
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| Friday, August 10, 2007 |
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9:00AM - 10:00AM |
Xiangjin Xu
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Xu-1
[Video available]
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The Institute is committed to the principles of Equal
Opportunity and Affirmative Action.
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