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Colloquia & Seminars


Current Seminars

  1. Hamiltonian Colloquium: Parity-time symmetry entails pseudo-Hermiticity regardless of diagonalizability

    Location: MSRI: Simons Auditorium
    Speakers: Hong Qin (Princeton University; University of Science and Technology of China)

    Parity-Time (PT)-symmetry, proposed by Bender and collaborators in the 1990s, is being actively studied as a fundamental property of quantum mechanics. It has also been applied to many other branches of physics. We prove that in finite dimensions PT-symmetric operators are necessarily pseudo-Hermitian, regardless of whether they are diagonalizable or not (arXiv:1801.01676). Pseudo-Hermitian operators, defined by Dirac and Pauli in 1940s, are equivalent to the G-Hamiltonian operators defined by Krein, Gelfand and collaborators in the 1950s. The confirmation of pseudo-Hermiticity for PT-symmetric operators enables the application of the Krein-collision theory to the study of spontaneous breaking of PT-symmetry. Specifically, we show that the physical mechanism of PT-symmetry breaking is the resonance between positive- and negative-action modes.

    Updated on Dec 04, 2018 12:29 PM PST

Upcoming Seminars

  1. Lunch with Hamilton: Construction of unstable KAM tori for a system of coupled NLS equations.

    Location: MSRI: Baker Board Room
    Speakers: Victor Vilaça Da Rocha (Basque Center for Applied Mathematics)

    The systems of coupled NLS equations occur in some physical problems, in particular in nonlinear optics (coupling between two optical waveguides, pulses or polarized components...). From the mathematical point of view, the coupling effects can lead to truly nonlinear behaviors, such as the beating effect (solutions with Fourier modes exchanging energy) of Grébert, Paturel and Thomann (2013).

    In this talk, I will use the coupling between two NLS equations on the 1D torus to construct a family of linearly unstable tori, and therefore unstable quasi-periodic solutions. The idea is to take profit of the Hamiltonian structure of the system via the construction of a Birkhoff normal form and the application of a KAM theorem. In particular, we will see of this surprising behavior (this is the first example of unstable tori for a 1D PDE) is strongly related to the existence of beating solutions. 

    This is a work in collaboration with Benoît Grébert (Université de Nantes).

    Updated on Dec 05, 2018 08:59 AM PST
  2. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  3. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  4. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  5. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  6. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  7. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  8. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  9. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  10. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  11. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  12. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  13. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  14. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST
  15. Combinatorics Seminar:

    Location: UC Berkeley Math (Evans Hall 939)
    Created on Nov 06, 2018 01:41 PM PST

Past Seminars

  1. Seminar Arnold Diffusion

    Created on Dec 05, 2018 03:17 PM PST
There are more then 30 past seminars. Please go to Past seminars to see all past seminars.