Zaher Hani Seminar: A Continuum Large Box Limit for the Cubic Nonlinear Schrödinger Equation

Analysis & Applied Math Seminar 2013-03-21 Speaker: Zaher Hani Institution: New York University Abstract: Inspired by the general paradigm of weak turbulence theory, we consider the 2D cubic nonlinear Schrödinger equation on a box of size L with periodic boundary conditions. In an appropriate “large box regime” (L very large), we derive a continuum equation on ℝ2 that governs the dynamics of the discrete frequency modes over nonlinear time scales. This equation turns out to satisfy many surprising symmetries and conservation laws, as well as several families of explicit solutions.
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Larry Guth Colloquium: Unexpected Applications of Polynomials in Combinatorics

My former colleague Larry Guth (now at MIT) visited us recently and gave a beautiful colloquium talk. The Department has recently deployed a video streaming service so we are able to share Larry’s talk with the world. We look forward to sharing other videos in the future.   Here is the video: Your browser does not support the <video> tag.     Unexpected applications of polynomials in combinatorics by Larry Guth | MIT Time: 16:10 (Wednesday, Jan.
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GWP of Gross-Pitaevskii Equation on R4

Last week, I had a chance to visit Edinburgh in part to serve as the external examiner on the PhD Thesis (papers) of Tim Candy. Tim is now Dr. Timothy Candy and has an exciting research program to develop as a postdoc at Imperial. It turned out I had lucky timing since my visit overlapped with a visit by Oana Pocovnicu. I had a chance to hear her speak about her recent work on the Gross-Pitaevskii equation.
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IAS Workshop on Symplectic Dynamics 2: Friday

IAS School of Mathematics   Workshop web page Friday: 2012-03-16 9:00 - 10:00 James Colliander, University of Toronto, “Big frequency cascades in the cubic nonlinear Schroedinger flow on the 2-torus” abstract 10:15 - 11:15 Marcel Guardia, IAS, “Growth of Sobolev norms for the cubic defocusing nonlinear Schroedinger equation in polynomial time” abstract 11:30 - 12:30 Yann Brenier, University of Nice, “Approximate geodesics on groups of volume preserving diffeomorphisms and adhesion dynamics” abstract James Colliander: Big frequency cascades in the cubic nonlinear Schrödinger flow on the 2-torus (chalk talk)
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IAS Workshop on Symplectic Dynamics 2: Thursday

IAS School of Mathematics   Workshop web page Thursday: 2012-03-15 9:00 - 10:00 Peter Topalov, Northeastern University, “Qualitative features of periodic solutions of KdV” abstract 10:15 - 11:15 Jiansheng Geng, Nanjing University, “Invariant tori for the nonlinear lattice one-dimensional Schroedinger equations with real analytic potential” abstract 11:30 - 12:30 Massimiliano Berti, UNINA, “Quasi periodic solutions of Hamiltonian PDEs” abstract 2:30 - 3:30 Ralph Saxton, University of New Orleans, “The generalized inviscid Proudman Johnson equation” abstract 4:30 - 5:30 Dongho Chae, Sungkyunkwan University, “On the blow-up problem for the Euler equations and the Liousville type results in the fluid equations” abstract Peter Topalov: Qualitative features of periodic solutions of KdV I need to do some detailed setup to expose the ideas I want to describe.
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IAS Workshop on Symplectic Dynamics 2: Wednesday

IAS School of Mathematics Workshop web page Happy Einstein Birthday! Wednesday: 2012-03-13 9:00 - 10:00 Wilfrid Gangbo, Georgia Institute of Technology, “Lifting absolutely continuous curves from P(Td) to P2(Rd)” abstract 10:15 - 11:15 Jonatan Lenells, Baylor University, “Geometry of diffeomorphism groupos, complete integrability and optimal transport” abstract 11:30 - 12:30 David Ebin, SUNY, “Groups of diffeomorphisms and geodesics on them” abstract 2:30 - 3:30 Susan Friedlander, University of Southern California, “Well / Ill-posedness results for the magneto-geostrophic equations: the importance of being even”.
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Princeton Math Colloquium: Soliton Resolution for the Radial Energy Critical Focusing Nonlinear Wave Equation

(Apologies for typos or misquotations…; please help me improve the post. –J. Colliander)   Princeton Math Colloquium 2012-03-14 Presenter: Carlos Kenig University of Chicago Title: A case study for critical non-linear dispersive equations: the energy critical wave equation Abstract: We will discuss recent work on the energy critical wave equation. The issues studied are global existence, scattering, finite time blow-up, universal profiles at blow-up and soliton resolution. This is viewed not as an isolated series of results, but as a way of approaching many similar critical non-linear dispersive equations.
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IAS Workshop on Symplectic Dynamics 2: Monday

I’m participating in a workshop at the Institute for Advanced Study on Symplectic Dynamics. This is part of the special concentration this year organized by Helmut Hofer. I’ll try to write notes on the talks I hear. Apologies to the speakers for typos and misquotations…. Comments (pending approval) are open for suggestions and edits. IAS School of Mathematics Workshop web page 10:15 - 11:15 Peter Constantin, Princeton University, “Long time, vanishing viscosity limits” abstract 11:30 - 12:30 Steve Preston, University of Colorado, “The inextensible string as a toy model of fluids” abstract 2:30 - 3:30 Emanuele Caglioti, University of Rome, “Long time behavior of solutions of Vlasov-like equations” abstract 4:30 - 5:30 Roberto Camassa, University of North Carolina, “Large amplitude internal waves and their stability” abstract Peter Constantin: Long time, vanishing viscosity limits (pdf slides) Navier-Stokes Navier-Stokes equations.
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IAS Workshop on Symplectic Dynamics 2: Tuesday

IAS School of Mathematics   Workshop web page Tuesday: 2012-03-13 9:00 - 10:00 Laszlo Szekelyhidi, University of Leipzig, “The h-principle for the Euler equations” abstract 10:15 - 11:15 Camilo de Lellis, University of Zurich, “The h-principle for the Euler equations Part 2” abstract 11:30 - 12:30 Vladimir Sverak, University of Minnesota, “On the long-time dynamics of some infinite-dimensional Hamiltonian systems” abstract 2:30 - 3:30 Antoine Choffrut, University of Leipzig, “On the local structure of the set of stationary flows to the 2D incompressible Euler equations” abstract 4:30 - 5:30 Thomas Kappeler, University of Zurich, “Symplectic techniques for integrable PDEs” abstract Laszlo Szekelyhidi: The h-principle for the Euler equations (chalk talk; joint work w.
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Academic Trendiness at AAAS

The American Association for the Advancement of Science is gathering for their Annual Meeting for 2012. One way to measure academic trendiness is to look at search frequencies of keywords using the search tool for the AAAS conference. “Basic Research” shows up 18 times; “Applied Research” shows up 93 times. “Africa” appears as frequently as “mathematics” and both appear less frequently than “warming” and “online”. “NSERC” appears as frequently as “Wellcome” and nearly 10 times less frequently than “NSF”.
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