Videos and presentation materials from other INI events are also available.
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 
Onedimensional quasiperiodic Schrödinger operators I
Quasiperiodic 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 ongoing 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," modelindependent 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 quasiperiodic 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 abovementioned 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 
KillipSimon 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 
Onedimensional quasiperiodic Schrödinger operators II
Quasiperiodic 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 ongoing 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," modelindependent 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 quasiperiodic 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 abovementioned 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 
Onedimensional quasiperiodic Schrödinger operators III
Quasiperiodic 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 ongoing 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," modelindependent 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 quasiperiodic 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 abovementioned 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 
Onedimensional quasiperiodic Schrödinger operators IV
Quasiperiodic 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 ongoing 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," modelindependent 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 quasiperiodic 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 abovementioned 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 
Onedimensional quasiperiodic Schrödinger operators V
Quasiperiodic 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 ongoing 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," modelindependent 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 quasiperiodic 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 abovementioned 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 
Onedimensional quasiperiodic Schrödinger operators VI
Quasiperiodic 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 ongoing 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," modelindependent 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 quasiperiodic 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 abovementioned 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 