2018-2019 - Autumn term programme

Sandrine Grellier (Orléans), Generic colourful tori and inverse spectral transform for Hankel operators
   5 October, 10:30-11:20, UCL (Room 706), Paris-London Analysis seminar

Tom Korner (Cambridge), Can we characterise sets of strong uniqueness
   5 October, 11:30-12:20, UCL (Room 706), London Analysis and Probability seminar

Emmanuel Fricain (Lille), Multipliers between sub-Hardy Hilbert spaces
   5 October, 14:00-14:50, UCL (Room 706), Paris-London Analysis seminar

♦ Tom Sanders (Oxford),The Erdös Moser sum-free set problem
   5 October, 15:20-16:10, UCL (Room 706), London Analysis and Probability seminar,

For abstracts of the talks please visit here

♠ Alexander Its (IUPUI), title of the talk
   11 October, 4:00-5:00, King's College London (Room S4.23), Analysis seminar

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Jürg Fröhlich (ETH), title TBA
   18 October, 3:00-4:00, UCL (Room tba), London Analysis and Probability seminar,

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Thomas Spencer (IAS), title TBA
   18 October, 4:30-5:30, UCL (Room tba), London Analysis and Probability seminar,

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♠ Jan Sbierski (Oxford), title of the talk
   25 October, 3:00-4:00, Imperial College (Huxley 140), Pure analysis and PDE seminar

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Thierry Lévy (Paris 6), title TBA
   1 November, 3:00-4:00, UCL (Room tba), London Analysis and Probability seminar,

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Name (Uni), title TBA
   1 November, 4:30-5:30, UCL (Room tba), London Analysis and Probability seminar,

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Vedran Sohinger (Warwick) Gibbs measures of nonlinear Schrödinger equations as limits of many-body quantum states in dimension d <= 3
   8 November, Imperial College (Huxley 140), Pure Analysis and PDE seminar

Abstract: Gibbs measures of nonlinear Schrödinger equations are a fundamental object used to study low-regularity solutions with random initial data. In the dispersive PDE community, this point of view was pioneered by Bourgain in the 1990s. We prove that Gibbs measures of nonlinear Schrödinger equations arise as high-temperature limits of appropriately modified thermal states in many-body quantum mechanics. We consider bounded defocusing interaction potentials and work either on the d-dimensional torus or on R^d with a confining potential. The analogous problem for d=1 and in higher dimensions with smooth non translation-invariant interactions was previously studied by Lewin, Nam, and Rougerie by means of variational techniques.
In our work, we apply a perturbative expansion of the interaction, motivated by ideas from field theory. The terms of the expansion are analysed using a diagrammatic representation and their sum is controlled using Borel resummation techniques. When d=2,3, we apply a Wick ordering renormalisation procedure. Moreover, in the one-dimensional setting our methods allow us to obtain a microscopic derivation of time-dependent correlation functions for the cubic nonlinear Schrödinger equation. This is joint work with Jürg Fröhlich, Antti Knowles, and Benjamin Schlein.

♠ Speaker (Uni), title of the talk
   15 November, 3:00-4:00, Imperial College (Huxley 140), Pure analysis and PDE seminar

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Jonathan Bennett (Birmingham) title TBA
   22 November, 3:00-4:00, UCL (Room tba), London Analysis and Probability seminar,

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♣ Herbert Koch (Bonn), title TBA,
   22 November, 4:30-5:30, UCL (Room tba), London Analysis and Probability seminar,

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♠ Speaker (Uni), title of the talk
   29 November, 3:00-4:00, Imperial College (Huxley 140), Pure analysis and PDE seminar

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Horst Knörrer (ETH) Construction of oscillatory singular homogenuous space times
   6 December, 3:00-4:00, UCL (Room tba), London Analysis and Probability seminar,

Abstract: The vacuum Einstein equations for Bianchi space times (that is space times that can be foliated into three dimensional space like slices that are all homogenuous spaces) reduce to a system of ordinary differential equations. The conjectures of Belinskii, Khalatnikov and Lifshitz predict that for almost all initial data the solutions of these differential equation behave like trajectories of a billiard in a Farey triangle in the hyperbolic plane, that is, a triangle whose three vertices are ideal points. In joint work with M.Reiterer and E.Trubowitz we show that, for a set of initial data that has positive measure, this is indeed the case. We use ideas inspired by scattering theory for approximations of the system. The fact that billiard in a Farey triangle is chaotic leads us to small divisor problems similiar to those of KAM theory in Hamiltonian dynamics.

Tuomas Sahsten (Manchester), title TBA
   6 December, 4:30-5:30, UCL (Room tba), London Analysis and Probability seminar,

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