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Seminars (PEPW01)

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Event When Speaker Title Presentation Material
PEPW01 5th January 2015
10:00 to 11:00
General spectral properties of ergodic operators I
PEPW01 5th January 2015
11:30 to 12:30
Introduction to periodic operators I
PEPW01 5th January 2015
13:30 to 14:30
Introduction to periodic operators II
PEPW01 5th January 2015
15:00 to 16:00
Random operators: multiscale analysis I
PEPW01 5th January 2015
16:00 to 17:00
Random operators: multiscale analysis II
PEPW01 6th January 2015
09:00 to 10:00
B Simon Orthogonal polynomials I
PEPW01 6th January 2015
10:00 to 11:00
B Simon Orthogonal polynomials II
PEPW01 6th January 2015
11:30 to 12:30
General spectral properties of ergodic operators II
PEPW01 6th January 2015
13:30 to 14:30
General spectral properties of ergodic operators III
PEPW01 6th January 2015
15:00 to 16:00
Introduction to periodic operators III
PEPW01 6th January 2015
16:00 to 17:00
Introduction to periodic operators IV
PEPW01 7th January 2015
09:00 to 10:00
General spectral properties of ergodic operators IV
PEPW01 7th January 2015
10:00 to 11:00
B Simon Orthogonal polynomials III
PEPW01 7th January 2015
11:30 to 12:30
B Simon Orthogonal polynomials IV
PEPW01 7th January 2015
13:30 to 14:30
Random operators: multiscale analysis III
PEPW01 7th January 2015
15:00 to 16:00
Random operators: multiscale analysis IV
PEPW01 7th January 2015
16:00 to 17:00
Introduction to periodic operators V
PEPW01 8th January 2015
09:00 to 10:00
F Klopp Random operators: many body problems I
The lectures will be devoted to the study of the thermodynamic limit of interacting fermions in a random background potential. We will restrict ourselves to the 0 temperature case. After discussing the case of non interacting fermions in a quite general setting, to understand the effect of interactions, we will specialize to various simple models where single particles are one dimensional.
PEPW01 8th January 2015
10:00 to 11:00
F Klopp Random operators: many body problems II
The lectures will be devoted to the study of the thermodynamic limit of interacting fermions in a random background potential. We will restrict ourselves to the 0 temperature case. After discussing the case of non interacting fermions in a quite general setting, to understand the effect of interactions, we will specialize to various simple models where single particles are one dimensional.
PEPW01 8th January 2015
11:30 to 12:30
F Klopp Random operators: many body problems III
The lectures will be devoted to the study of the thermodynamic limit of interacting fermions in a random background potential. We will restrict ourselves to the 0 temperature case. After discussing the case of non interacting fermions in a quite general setting, to understand the effect of interactions, we will specialize to various simple models where single particles are one dimensional.
PEPW01 8th January 2015
13:30 to 14:30
Random operators: multiscale analysis V
PEPW01 8th January 2015
15:00 to 16:00
Random operators: multiscale analysis VI
PEPW01 8th January 2015
16:00 to 17:00
Introduction to periodic operators VI
PEPW01 9th January 2015
09:00 to 10:00
F Klopp Random operators: many body problems IV
The lectures will be devoted to the study of the thermodynamic limit of interacting fermions in a random background potential. We will restrict ourselves to the 0 temperature case. After discussing the case of non interacting fermions in a quite general setting, to understand the effect of interactions, we will specialize to various simple models where single particles are one dimensional.
PEPW01 9th January 2015
10:00 to 11:00
F Klopp Random operators: many body problems V
The lectures will be devoted to the study of the thermodynamic limit of interacting fermions in a random background potential. We will restrict ourselves to the 0 temperature case. After discussing the case of non interacting fermions in a quite general setting, to understand the effect of interactions, we will specialize to various simple models where single particles are one dimensional.
PEPW01 9th January 2015
11:30 to 12:30
F Klopp Random operators: many body problems VI
The lectures will be devoted to the study of the thermodynamic limit of interacting fermions in a random background potential. We will restrict ourselves to the 0 temperature case. After discussing the case of non interacting fermions in a quite general setting, to understand the effect of interactions, we will specialize to various simple models where single particles are one dimensional.
PEPW01 9th January 2015
13:30 to 14:30
Periodic operators: the method of gauge transform I
PEPW01 9th January 2015
15:00 to 16:00
Random operators: multiscale analysis VII
PEPW01 9th January 2015
16:00 to 17:00
Random operators: multiscale analysis VIII
PEPW01 12th January 2015
13:30 to 14:30
Periodic operators: the method of gauge transform II
PEPW01 12th January 2015
15:00 to 16:00
Periodic operators: the method of gauge transform III
PEPW01 12th January 2015
16:00 to 17:00
Periodic operators: the method of gauge transform IV
PEPW01 12th January 2015
17:00 to 18:30
B Simon Tales of Our Forefathers
PEPW01 13th January 2015
09:00 to 10:00
B Simon Orthogonal polynomials V
PEPW01 13th January 2015
10:00 to 11:00
B Simon Orthogonal polynomials VI
PEPW01 13th January 2015
11:30 to 12:30
One-dimensional quasi-periodic Schrödinger operators I
Quasi-periodic Schrödinger operators arise in solid state physics, describing the influence of an external magnetic field on the electrons of a crystal. In the late 1970s, numerical studies for the most prominent model, the almost Mathieu operator (AMO), produced the first example of a fractal in physics known as "Hofstadter's butterfly," marking the starting point for the on-going strong interest in such operators in both mathematics and physics. Whereas research in the first three decades was focussed mainly on unraveling the unusual properties of the AMO, in recent years a combination of techniques from dynamical systems with those from spectral theory has allowed for a more "global," model-independent point of view. Intriguing phenomena first encountered for the AMO, notably the appearance of a critical phase corresponding to purely singular continuous spectrum, could be tested for their prevalence in general models. This workshop will introduce the participants to some of the techniques necessary to understand the spectral properties of quasi-periodic Schrödinger operators. The presentation is of expository nature and will particularly emphasize the close ties to dynamical systems (``matrix cocycles''), which was successfully used to address several open problems (e.g. the ``Ten Martini problem'') and enabled above-mentioned global perspective.

Topics included are: Basics: collectivity and regularity of spectral properties, matrix cocycles, arithmetic conditions Lyapunov exponent: positivity and continuity Supercritical behavior - Anderson localization Subcritical behavior - Duality, reducibility, and absolutely continuous spectrum Avila's global theory and critical behavior

PEPW01 14th January 2015
11:30 to 12:30
Killip-Simon problem and Jacobi flow on GSMP matrices
PEPW01 14th January 2015
13:30 to 14:30
B Simon Orthogonal polynomials VII
PEPW01 14th January 2015
15:00 to 16:00
B Simon Orthogonal polynomials VIII
PEPW01 14th January 2015
16:00 to 17:00
One-dimensional quasi-periodic Schrödinger operators II
Quasi-periodic Schrödinger operators arise in solid state physics, describing the influence of an external magnetic field on the electrons of a crystal. In the late 1970s, numerical studies for the most prominent model, the almost Mathieu operator (AMO), produced the first example of a fractal in physics known as "Hofstadter's butterfly," marking the starting point for the on-going strong interest in such operators in both mathematics and physics. Whereas research in the first three decades was focussed mainly on unraveling the unusual properties of the AMO, in recent years a combination of techniques from dynamical systems with those from spectral theory has allowed for a more "global," model-independent point of view. Intriguing phenomena first encountered for the AMO, notably the appearance of a critical phase corresponding to purely singular continuous spectrum, could be tested for their prevalence in general models. This workshop will introduce the participants to some of the techniques necessary to understand the spectral properties of quasi-periodic Schrödinger operators. The presentation is of expository nature and will particularly emphasize the close ties to dynamical systems (``matrix cocycles''), which was successfully used to address several open problems (e.g. the ``Ten Martini problem'') and enabled above-mentioned global perspective.

Topics included are: Basics: collectivity and regularity of spectral properties, matrix cocycles, arithmetic conditions Lyapunov exponent: positivity and continuity Supercritical behavior - Anderson localization Subcritical behavior - Duality, reducibility, and absolutely continuous spectrum Avila's global theory and critical behavior

PEPW01 15th January 2015
09:00 to 10:00
Periodic operators: the method of gauge transform V
PEPW01 15th January 2015
10:00 to 11:00
Periodic operators: the method of gauge transform VI
PEPW01 15th January 2015
11:30 to 12:30
One-dimensional quasi-periodic Schrödinger operators III
Quasi-periodic Schrödinger operators arise in solid state physics, describing the influence of an external magnetic field on the electrons of a crystal. In the late 1970s, numerical studies for the most prominent model, the almost Mathieu operator (AMO), produced the first example of a fractal in physics known as "Hofstadter's butterfly," marking the starting point for the on-going strong interest in such operators in both mathematics and physics. Whereas research in the first three decades was focussed mainly on unraveling the unusual properties of the AMO, in recent years a combination of techniques from dynamical systems with those from spectral theory has allowed for a more "global," model-independent point of view. Intriguing phenomena first encountered for the AMO, notably the appearance of a critical phase corresponding to purely singular continuous spectrum, could be tested for their prevalence in general models. This workshop will introduce the participants to some of the techniques necessary to understand the spectral properties of quasi-periodic Schrödinger operators. The presentation is of expository nature and will particularly emphasize the close ties to dynamical systems (``matrix cocycles''), which was successfully used to address several open problems (e.g. the ``Ten Martini problem'') and enabled above-mentioned global perspective.

Topics included are: Basics: collectivity and regularity of spectral properties, matrix cocycles, arithmetic conditions Lyapunov exponent: positivity and continuity Supercritical behavior - Anderson localization Subcritical behavior - Duality, reducibility, and absolutely continuous spectrum Avila's global theory and critical behavior

PEPW01 16th January 2015
13:30 to 14:30
One-dimensional quasi-periodic Schrödinger operators IV
Quasi-periodic Schrödinger operators arise in solid state physics, describing the influence of an external magnetic field on the electrons of a crystal. In the late 1970s, numerical studies for the most prominent model, the almost Mathieu operator (AMO), produced the first example of a fractal in physics known as "Hofstadter's butterfly," marking the starting point for the on-going strong interest in such operators in both mathematics and physics. Whereas research in the first three decades was focussed mainly on unraveling the unusual properties of the AMO, in recent years a combination of techniques from dynamical systems with those from spectral theory has allowed for a more "global," model-independent point of view. Intriguing phenomena first encountered for the AMO, notably the appearance of a critical phase corresponding to purely singular continuous spectrum, could be tested for their prevalence in general models. This workshop will introduce the participants to some of the techniques necessary to understand the spectral properties of quasi-periodic Schrödinger operators. The presentation is of expository nature and will particularly emphasize the close ties to dynamical systems (``matrix cocycles''), which was successfully used to address several open problems (e.g. the ``Ten Martini problem'') and enabled above-mentioned global perspective.

Topics included are: Basics: collectivity and regularity of spectral properties, matrix cocycles, arithmetic conditions Lyapunov exponent: positivity and continuity Supercritical behavior - Anderson localization Subcritical behavior - Duality, reducibility, and absolutely continuous spectrum Avila's global theory and critical behavior

PEPW01 16th January 2015
15:00 to 16:00
One-dimensional quasi-periodic Schrödinger operators V
Quasi-periodic Schrödinger operators arise in solid state physics, describing the influence of an external magnetic field on the electrons of a crystal. In the late 1970s, numerical studies for the most prominent model, the almost Mathieu operator (AMO), produced the first example of a fractal in physics known as "Hofstadter's butterfly," marking the starting point for the on-going strong interest in such operators in both mathematics and physics. Whereas research in the first three decades was focussed mainly on unraveling the unusual properties of the AMO, in recent years a combination of techniques from dynamical systems with those from spectral theory has allowed for a more "global," model-independent point of view. Intriguing phenomena first encountered for the AMO, notably the appearance of a critical phase corresponding to purely singular continuous spectrum, could be tested for their prevalence in general models. This workshop will introduce the participants to some of the techniques necessary to understand the spectral properties of quasi-periodic Schrödinger operators. The presentation is of expository nature and will particularly emphasize the close ties to dynamical systems (``matrix cocycles''), which was successfully used to address several open problems (e.g. the ``Ten Martini problem'') and enabled above-mentioned global perspective.

Topics included are: Basics: collectivity and regularity of spectral properties, matrix cocycles, arithmetic conditions Lyapunov exponent: positivity and continuity Supercritical behavior - Anderson localization Subcritical behavior - Duality, reducibility, and absolutely continuous spectrum Avila's global theory and critical behavior

PEPW01 16th January 2015
16:00 to 17:00
One-dimensional quasi-periodic Schrödinger operators VI
Quasi-periodic Schrödinger operators arise in solid state physics, describing the influence of an external magnetic field on the electrons of a crystal. In the late 1970s, numerical studies for the most prominent model, the almost Mathieu operator (AMO), produced the first example of a fractal in physics known as "Hofstadter's butterfly," marking the starting point for the on-going strong interest in such operators in both mathematics and physics. Whereas research in the first three decades was focussed mainly on unraveling the unusual properties of the AMO, in recent years a combination of techniques from dynamical systems with those from spectral theory has allowed for a more "global," model-independent point of view. Intriguing phenomena first encountered for the AMO, notably the appearance of a critical phase corresponding to purely singular continuous spectrum, could be tested for their prevalence in general models. This workshop will introduce the participants to some of the techniques necessary to understand the spectral properties of quasi-periodic Schrödinger operators. The presentation is of expository nature and will particularly emphasize the close ties to dynamical systems (``matrix cocycles''), which was successfully used to address several open problems (e.g. the ``Ten Martini problem'') and enabled above-mentioned global perspective.

Topics included are: Basics: collectivity and regularity of spectral properties, matrix cocycles, arithmetic conditions Lyapunov exponent: positivity and continuity Supercritical behavior - Anderson localization Subcritical behavior - Duality, reducibility, and absolutely continuous spectrum Avila's global theory and critical behavior

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons