2011 Winter CMS Meeting Notes

This past weekend, I attended the 2011 Winter meeting of the Canadian Mathematical Society. I have posted below some (often rough) notes on the talks that I attended. Robert McCann (joint work with J. Denzler and H. Koch) ROBERT MCCANN, University of Toronto Higher-order asymptotics of fast diffusion in Euclidean space: a dynamical systems approach. With Denzler and Koch, we quantify the speed of convergence and higher-order asymptotics of fast diffusion dynamics on Rn to the Barenblatt (self similar) solution.
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2011 Winter CMS Town Hall Notes

The 2011 Winter CMS Meeting took place this past weekend. On Sunday (2011-12-11), there was a CMS Town Hall meeting. The discussion was led by a panel consisting of Long Range Plan Committee Chair Nancy Reid, CMS President Jacques Hurtubise, and CMS Director Johan Rudnick (who was partially obscured by a poinsetta). Attendees to the town hall meeting were fed a free lunch. Long Range Plan Update Nancy gave a status update on the long range plan.
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Addendum to Arnold Memorial Workshop: Khesin on Pinzari Talk

  The following message is a guest post by Boris Khesin. Boris summarizes the wonderful talk given by Gabriella Pinzari at the workshop. –Jim Colliander Gabriella Pinzari (30min talk) described her joint result with her advisor Luigi Chierchia on a recently found fix for the famous KAM theorem, or rather for its application to the stability of the Solar system. Namely, the original KAM theorem inArnold’s 1963 paper claimed the persistence of the Liouville tori for perturbations of integrable systems under some nondegeneracy assumption - some determinant must be nonzero.
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Edinburgh Arnold Memorial Workshop Notes

I am at an interesting workshop in Edinburgh entitled Dynamical systems and classical mechanics: a conference in celebration of Vladimir Arnold 1937 - 2010. Boris Khesin and Serge Tabachnikov have coordinated a Tribute to Vladimir Arnold which will soon appear in consecutive issues of the Notices of the AMS. These tributes were shared at the workshop and are also available here: Arnold1 Arnold2 I will post below my notes from the talks.
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Île de Berder Workshop Notes

I am at a workshop on Île de Berder. The post below contains the notes I am taking during the talks. I apologize (especially to the speakers) for misquotations and typos but I hope the notes might be useful. Tuesday 2011-09-06 Rafik Imekraz: Non resonant normal form for perturbed quantum harmonic oscillator Study high sobolev norms of solutions $\psi$ solving a NLS with harmonic trap and a nice smooth bounded potential.
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Edinburgh Meeting Notes 3

Galina Perelman: 2 soliton collision in NLS $$ i \partial_t \psi = - \psi_{xx} + F(|\psi|^2) \psi, ~ x \in R $$ where $F(\xi) = -2 \xi + O (\xi^2), ~ \xi \rightarrow 0.$ This family of equations has solitary wave solutions $$ e^{i \theta(x,t) \phi (x - b(t), E)} $$ where $\theta(x,t) = \omega t + \gamma + v \frac{x}{2}, ~b(t) =vt + c$ (all reall parameters). The profile $\phi$ is the associated ground state, which is $C^2$, decays exponentially, is even, …
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Edinburgh Meeting Notes 2

Sergei Kuksin (École Polytechnique): Nonlinear Schrödinger Equation We consider Hamiltonian PDE. This is of course very interesting. In physics, there is a class of pdes which is also of interest: Hamiltonian PDE = small damping + small forcing Why is it so important? This class contains a very important equation: Navier-Stokes. $$ \dot{u} + (u\cdot \nabla) u + \nabla p = \epsilon \Delta u + force; ~ \nabla \cdot u = 0.
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Edinburgh Meeting Notes 1

These are notes from a meeting entitled Advanced Numerical Studies in Nonlinear PDEs in Edinburgh, Scotland. Walter Craig (McMaster): Water Wave Interactions I’m an analyst but I’m going to talk about numerics and experiments as well as analysis. We will discuss the problem of water waves and then I’ll talk about two specific settings in which the theory has led to good and quite elegant numerics and the numerics have started to answer some questions.
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Notes on Nonlinear Dispersive Equations Workshop in Istanbul

During last week’s NDE meeting in Istanbul, I experimented and took real-time notes in MultiMarkDown during the talks. If any of the speakers wish, I can post links to their presentations provided they send me a copy of their slides. –J. Colliander James Colliander (Toronto) Almost sure well-posedness of the cubic nonlinear Schrödinger equation below $L^2({\mathbb{T}})$ I spoke about recent work with Hiro Oh . Here is alink to my slides.
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