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The pseudoconformal and conformal transformations
Consider the free Schrödinger equation in spatial dimensions, which I will normalise as where is the unknown field and is the spatial Laplacian. To avoid irrelevant technical issues I will restri… more →
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The pseudoconformal and conformal transformations
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wrote 3 months ago: Consider the free Schrödinger equation in spatial dimensions, which I will normalise as where i … more →
Some notes on Bakry-Emery theory
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wrote 3 months ago: [These are notes intended mostly for myself, as these topics are useful in random matrix theory, but … more →
Lars Hormander
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wrote 5 months ago: Lars Hörmander, who made fundamental contributions to all areas of partial differential equatio … more →
A direct proof of the stationarity of the Dyson sine process under Dyson Brownian motion
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wrote 6 months ago: Let be a large natural number, and let be a matrix drawn from the Gaussian Unitary Ensemble (GUE), b … more →
The spectral theorem and its converses for unbounded symmetric operators
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wrote 1 year ago: Let be a self-adjoint operator on a finite-dimensional Hilbert space . The behaviour of this operato … more →
254B, Notes 3: Quasirandom groups, expansion, and Selberg's 3/16 theorem
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wrote 1 year ago: In the previous set of notes we saw how a representation-theoretic property of groups, namely Kazhda … more →
A correction to "Localisation and compactness properties of the Navier-Stokes global regularity problem"
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wrote 1 year ago: A few days ago, I released a preprint entitled “Localisation and compactness properties of the … more →
Localisation and compactness properties of the Navier-Stokes global regularity problem
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wrote 1 year ago: I’ve just uploaded to the arXiv my paper “Localisation and compactness properties of the … more →
The limiting absorption principle
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wrote 2 years ago: Perhaps the most fundamental differential operator on Euclidean space is the Laplacian The Laplacian … more →
The shallow water wave equation and tsunami propagation
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wrote 2 years ago: As we are all now very much aware, tsunamis are water waves that start in the deep ocean, usually be … more →
The mesoscopic structure of GUE eigenvalues
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wrote 2 years ago: This week I am at the American Institute of Mathematics, as an organiser on a workshop on the univer … more →
Concentration compactness via nonstandard analysis
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wrote 2 years ago: One of the key difficulties in performing analysis in infinite-dimensional function spaces, as oppos … more →
Asymptotic decay for a one-dimensional nonlinear wave equation
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wrote 2 years ago: Hans Lindblad and I have just uploaded to the arXiv our joint paper “Asymptotic decay for a on … more →
Spielman, Meyer, Nirenberg
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wrote 2 years ago: In my previous post, I briefly discussed the work of the four Fields medalists of 2010 (Lindenstraus … more →
Lindenstrauss, Ngo, Smirnov, Villani
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wrote 2 years ago: As is now widely reported, the Fields medals for 2010 have been awarded to Elon Lindenstrauss, Ngo B … more →
The uncertainty principle
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wrote 2 years ago: A recurring theme in mathematics is that of duality: a mathematical object can either be described i … more →
The Euler-Arnold equation
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wrote 2 years ago: A (smooth) Riemannian manifold is a smooth manifold without boundary, equipped with a Riemannian met … more →
Amplitude-frequency dynamics for semilinear dispersive equations
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wrote 3 years ago: Semilinear dispersive and wave equations, of which the defocusing nonlinear wave equation is a typic … more →
254A, Notes 6: Gaussian ensembles
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wrote 3 years ago: Our study of random matrices, to date, has focused on somewhat general ensembles, such as iid random … more →
