Simons Lecture III: Structure and randomness in PDE
[This lecture is also doubling as this week's "open problem of the week", as it (eventually) discusses the soliton resolution conjecture.] In this third lecture, I will talk about how the dichotomy...
View ArticleThe cubic nonlinear Schrödinger equation in two dimensions with radial data
I’ve just uploaded to the arXiv the paper “The cubic nonlinear Schrödinger equation in two dimensions with radial data“, joint with Rowan Killip and Monica Visan, and submitted to the Annals of...
View ArticleConcentration compactness and the profile decomposition
One of the most important topological concepts in analysis is that of compactness (as discussed for instance in my Companion article on this topic). There are various flavours of this concept, but let...
View ArticleConcentration compactness via nonstandard analysis
One of the key difficulties in performing analysis in infinite-dimensional function spaces, as opposed to finite-dimensional vector spaces, is that the Bolzano-Weierstrass theorem no longer holds: a...
View ArticleLocalisation and compactness properties of the Navier-Stokes global...
I’ve just uploaded to the arXiv my paper “Localisation and compactness properties of the Navier-Stokes global regularity problem“, submitted to Analysis and PDE. This paper concerns the global...
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