Vũ Ngọc San

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Research

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lundi 28 septembre 2009

Constructing semitoric integrable systems.

Par San Vu Ngoc le lundi 28 septembre 2009, 15:45

With Álvaro Pelayo, we have answered the question naturally raised by our previous work, when we made explicit a complete set of symplectic invariants for semitoric systems.

The article will appear in Acta Mathematica.

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mardi 11 août 2009

Semitoric integrable systems on symplectic 4-manifolds

Par San Vu Ngoc le mardi 11 août 2009, 20:19

Here is an article we wrote with A. Pelayo in June 2008. I find it an interesting and natural result combining ideas from hamiltonian torus actions and the symplectic geometry of integrable systems.

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jeudi 28 mai 2009

Rencontre ANR NONAa à Rennes 3-4 juin 2009

Par San Vu Ngoc le jeudi 28 mai 2009, 10:09

Réunion de l’ANR Analyse spectrale et microlocale d’opérateurs non autoadjoints

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mercredi 19 décembre 2007

Research interests

Par San Vu Ngoc le mercredi 19 décembre 2007, 21:52

My research interests are centred on the one hand on microlocal and semiclassical analysis (à la Duistermaat-Hörmander, Robert, Helffer, Sjöstrand, etc.) of hamiltonian systems, with a specific focus on integrable and near-integrable systems, and on the other hand on related symplectic geometry topics.

More generally, I am naturally attracted by problems combining geometry and analysis, and building bridges between maths and physics.

Here are the current mathematical topics I am involved in:
  • Singularities of completely integrable systems. Normal forms, symplectic classification.
  • Atiyah and Guillemin-Sternberg's moment polytopes, Delzant theorem.
  • Establishing strong links between symplectic invariants and quantum spectra of commuting microlocal operators (pseudo-differential, or Toeplitz). Quantum versions of monodromy and Chern class of integrable systems.
  • Semiclassical and WKB analysis.
  • Birkhoff normal forms, and quantum reduction.
  • Non self-adjoint operators, pseudo-spectra.
  • Almost integrable systems, KAM theory.
  • Long time behaviour of semiclassical wave packets, revivals.

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lundi 17 décembre 2007

Quantum Birkhoff normal forms and semiclassical analysis

Par San Vu Ngoc le lundi 17 décembre 2007, 15:02


If you don't feel like reading the original article, you might want to have a look at this. This is a written version of a talk I delivered at IHES in November 2006.

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