PEP
5 January 2015 to 26 June 2015
The main objective of the programme is to bring together specialists in periodic, almost- periodic and random problems to discuss recent developments and deep connections between the methods intrinsic for each of these research areas. In the last several years there emerged a number of methods that had originated in one of these topics (e.g. periodic or random operators) but later were successfully used to tackle problems in a parallel area (e.g. almost-periodic). This suggests that these three lines of research have more in common than previously believed, and the interaction between specialists working in each of these areas could lead to a better understanding of ergodic operators and take us closer to solving open problems.
The programme will thus have three major themes: periodic, almost-periodic, and random operators acting in Rd or Zd; operators on manifolds or graphs and more general ergodic operators will be also considered. We also intend to address problems that lie at the interface of the main topics (e.g. "sheared" periodic operators), and applications in other areas of mathematics (e.g. geometry).
At the beginning of the programme, there will be a two-week long instructional conference with six mini-courses of about ten lectures each. The courses will be designed for students and non-specialists, and will be organised in order to make them accessible to the UK community. Further there will be three workshops evenly spread over the period of the programme to cover more advanced results, each centred around one of the main themes of the programme. However, we do not plan to make these workshops too specialised, and expect that all three themes will be prominently represented at each of them. We plan to organise the programme in such a way that at any time a mixture of experts from at least two areas will be present at the Institute.
The programme has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 291147.
Click here to download the programme's final scientific report
Title | Year | Programme | |
---|---|---|---|
Killip-Simon problem and Jacobi flow on GSMP matricesAuthors: Peter Yuditskii |
2014 | PEP | 21 October 2016 |
Generalized linear Boltzmann equations for particle transport in polycrystalsAuthors: J Marklof, A Strombergsson |
2014 | PEP | 21 October 2016 |
Quadratic Weyl sums, automorphic functions, and invariance principlesAuthors: F Cellarosi, J Marklof |
2014 | PEP | 21 October 2016 |
Spectral honogeneity of limit-periodic Schrödinger operatorsAuthors: Jake Fillman, M Lukic |
2014 | PEP | 21 October 2016 |
Generalized Prüfer variables for perturbations of Jacobi and CMV matricesAuthors: M Lukic, DC Ong |
2014 | PEP | 21 October 2016 |
Fractional Brownian motion with Hurst index H=0 and the Gaussian Unitary EnsembleAuthors: YV Fyodorov, Boris Khoruzhenko, NJ Simm |
2014 | PEP | 21 October 2016 |
Accumulation of complex eigenvalues of an indefinite Sturm-Liouville operator with a shifted Coulomb potentialAuthors: M Levitin, Marcello Seri |
2014 | PEP | 21 October 2016 |
From constant to non-degenerately vanishing magnetic fields in superconductivityAuthors: B Helffer, A Kachmar |
2014 | PEP | 21 October 2016 |
Mixed spectral regimes for square Fibonacci HamiltoniansAuthors: Jake Fillman, Y Takahash, W Yessen |
2014 | PEP | 21 October 2016 |
Chamber's forumla for the graphene and the Hou model with kagome periodicity and applicationsAuthors: B Helffer, P Kerdelhue, J Royo-Letelier |
2014 | PEP | 21 October 2016 |
Exponential scaling limit of the single-particle Anderson model via adaptive feedback scalingAuthors: V Chulaevsky |
2014 | PEP | 21 October 2016 |
Efficient localization bounds in a continuous N-particle Anderson model with long-range interactionAuthors: V Chulaevsky |
2014 | PEP | 21 October 2016 |
Asymptotics for Erd?s-Solojev zero modes in strong fieldsAuthors: Daniel Mark Elton |
2014 | PEP | 21 October 2016 |
Mixed spectral types for one frequency discrete quasi-periodic Schrödinger operatorAuthors: S Zhang |
2014 | PEP | 21 October 2016 |
$\it L$$^2$-Reducibility and localization for quasiperiodic operatorsAuthors: S Jitomirskaya, Ilya Kachkovskiy |
2014 | PEP | 21 October 2016 |
A uniform area law for the entanglement of eigenstates in the disordered XY chainAuthors: H Abdul-rahman, Gunter Stolz |
2014 | PEP | 21 October 2016 |
Magnetic wells in dimension threeAuthors: B Helffer, Y Kordyukov, N Raymond, S Vu Ngoc |
2014 | PEP | 21 October 2016 |
Mixed normal-superconducting states in the presence of strong electric currentsAuthors: Y Almog, B Helffer, XB Pan |
2014 | PEP | 21 October 2016 |
Lower bound for the number of critical points of minimal spectral $\it k$-partitions for $\it k$ large.Authors: B Helffer |
2014 | PEP | 21 October 2016 |
On transport properties of isotropic quasiperiodic $\it XY$ spin chainsAuthors: Ilya Kachkovskiy |
2014 | PEP | 21 October 2016 |
Complete exponential localization in a discrete multi-particle Anderson model with interaction of infinite rangeAuthors: V Chulaevsky |
2014 | PEP | 21 October 2016 |
Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channelAuthors: Christian Sadel |
2014 | PEP | 21 October 2016 |
Invariance principle for the periodic Lorentz gas in the Boltzmann-Grad limitAuthors: J Marklof, B Toth |
2014 | PEP | 21 October 2016 |
Green's function asymptotics near the internal edges of spectra of periodic elliptic operators: spectral gap interior.Authors: M Kha, Peter Kuchment, A Raich |
2014 | PEP | 21 October 2016 |
On the phase-space distribution of Bloch eigenmodes for periodic point scatterersAuthors: J Griffin |
2014 | PEP | 21 October 2016 |
Exponential Riemann sums and "near" -quasicrystalsAuthors: Toshikazu Sunada |
2014 | PEP | 21 October 2016 |
Ballistic transport for the Schrödinger operator with limit-periodic or quasi-periodic potential in dimension twoAuthors: Yulia Karpeshina, Young-Ran Lee, Roman Shterenberg, Gunter Stolz |
2014 | PEP | 21 October 2016 |
Localization principle for compact Hankel operatorsAuthors: A Pushnitski, Dimitri Yafaev |
2014 | PEP | 21 October 2016 |
Homogenization of nonstationary Schrödinger type equations with periodic coefficientsAuthors: Tatiana Suslina |
2014 | PEP | 21 October 2016 |
Two-scale series expansions for travelling wave packets in one-dimensional periodic mediaAuthors: KD Cherednichenko |
2014 | PEP | 21 October 2016 |
A sub-Riemannian Santaló formula with applications to isoperimetric inequalities and Dirichlet spectral gap of hypoelliptic operatorsAuthors: D Prandi, L Rizzi, Marcello Seri |
2014 | PEP | 21 October 2016 |
An overview of periodic elliptic operatorsAuthors: Peter Kuchment |
2014 | PEP | 21 October 2016 |
On the structure of band edges of 2D periodic elliptic operatorsAuthors: Nikolai Filonov, Ilya Kachkovskiy |
2014 | PEP | 21 October 2016 |
Best rational approximation of functions with logarithmic singularitiesAuthors: A Pushnitski, Dimitri Yafaev |
2014 | PEP | 21 October 2016 |
Almost periodicity in time of solutions of the KDV equationAuthors: I Binder, David Damanik, Michael Goldstein, M Lukic |
2014 | PEP | 21 October 2016 |
Limit-Periodic continuum Schödinger operators with zero measure Cantor spectrumAuthors: David Damanik, Jake Fillman, M Lukic |
2014 | PEP | 21 October 2016 |
Characterization of the metal-insulator transport transition for the two-particle Anderson modelAuthors: A Klein, ST Nguyen, C Rojas-molina |
2014 | PEP | 21 October 2016 |
5 January 2015 to 16 January 2015
23 March 2015 to 27 March 2015
7 April 2015 to 10 April 2015
22 June 2015 to 26 June 2015
Sunday 9th February 2014 | |||
---|---|---|---|
14:00 to 15:00 | Room 1 |
Wednesday 21st January 2015 | |||
---|---|---|---|
16:00 to 17:00 |
Applications of Jacobi matrices to propagation in the XY spin chain |
Room 2 |
Tuesday 3rd February 2015 | |||
---|---|---|---|
14:00 to 15:00 |
Discrete spectrum of Schroedinger operators with oscillating decaying potentials |
Room 2 | |
Thursday 5th February 2015 | |||
---|---|---|---|
11:00 to 12:00 |
Behaviour of zero modes for a one-dimensional Dirac operator arising in models of graphene |
Room 2 | |
Wednesday 11th February 2015 | |||
---|---|---|---|
14:00 to 15:00 |
Schrodinger or Pauli operators with self-generated magnetic fields |
Room 1 | |
Tuesday 24th February 2015 | |||
---|---|---|---|
14:00 to 15:00 |
Accumulation of complex eigenvalues for a class of indefinite Sturm-Liouville operators |
Room 2 | |
Wednesday 25th February 2015 | |||
---|---|---|---|
14:00 to 15:00 |
On the minimax principle for eigenvalues of Dirac operator with Coulombic singularities |
Room 2 | |
Tuesday 3rd March 2015 | |||
---|---|---|---|
14:00 to 15:00 |
Negative eigenvalues of two-dimensional Schroedinger operators |
Room 2 | |
Wednesday 4th March 2015 | |||
---|---|---|---|
14:00 to 15:00 |
Resolvent estimates for high-contrast elliptic problems with periodic coefficients |
Room 2 | |
Thursday 12th March 2015 | |||
---|---|---|---|
14:00 to 15:00 |
Uncertainty principles and spectral analysis of Schroedinger operators |
Room 2 | |
Tuesday 17th March 2015 | |||
---|---|---|---|
12:30 to 13:30 |
Eigenvalue statistics for a class of non-self-adjoint operators under random perturbations |
Room 2 | |
Wednesday 18th March 2015 | |||
---|---|---|---|
16:40 to 17:40 |
Fractional Brownian Motion with zero Hurst index and GUE random matrices |
Room 1 |
Monday 23rd March 2015 | |||
---|---|---|---|
09:00 to 09:50 | No Room Required | ||
09:50 to 10:00 | Room 1 | ||
10:00 to 11:00 | Room 1 | |
|
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
Uncertainty relations and Wegner estimates for random breather potentials |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 | Room 1 | |
|
14:30 to 15:00 | No Room Required | ||
15:00 to 16:00 | Room 1 | |
|
16:00 to 17:00 |
Entanglement in the disordered XY spin chain and open problems for random block operators |
Room 1 | |
17:00 to 18:00 | No Room Required |
Tuesday 24th March 2015 | |||
---|---|---|---|
10:00 to 11:00 |
Diophantine properties and the spectral theory of explicit quasiperiodic models |
Room 1 | |
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 | Room 1 | |
|
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 |
Perturbative methods for Schrödinger operator: from periodic to quasiperiodic potentials. |
Room 1 | |
14:30 to 15:00 | No Room Required | ||
15:00 to 16:00 |
Spectral statistics of Bernoulli matrix ensembles - a random walk approach |
Room 1 | |
16:00 to 17:00 | Room 1 | |
Wednesday 25th March 2015 | |||
---|---|---|---|
09:00 to 17:00 | No Room Required | ||
10:00 to 11:00 | Room 1 | |
|
11:00 to 11:30 | No Room Required | ||
11:00 to 11:30 | No Room Required | ||
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
Some connections between Weyl-Titchmarsh theory, oscillation theory, and density of states |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 |
Local Density of States and the Spectral Function for Quasi-Periodic Operators |
Room 1 | |
14:30 to 15:00 | No Room Required | ||
15:00 to 16:00 | Room 1 | |
|
16:00 to 17:00 |
Chambers formulas and semiclassical analysis for generalized Harper's butterflies |
Room 1 | |
Thursday 26th March 2015 | |||
---|---|---|---|
10:00 to 11:00 | Room 1 | |
|
11:00 to 11:30 | No Room Required | ||
11:00 to 11:30 | No Room Required | ||
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
Two-scale 'micro-resonant' homogenisation of periodic (and some ergodic) problems |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
19:30 to 22:00 | No Room Required |
Friday 27th March 2015 | |||
---|---|---|---|
10:00 to 11:00 |
Operator error estimates for homogenization of elliptic systems with periodic coefficients |
Room 1 | |
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
Wannier functions for periodic Schrödinger operators and harmonic maps into the unitary group |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 |
Everywhere discontinuous anisotropy of thin periodic composite plates |
Room 1 | |
14:30 to 15:00 | No Room Required | ||
15:00 to 16:00 | Room 1 | |
|
16:00 to 17:00 |
On the gaps in the spectrum of the periodic Maxwell operator |
Room 1 | |
Monday 30th March 2015 | |||
---|---|---|---|
12:30 to 13:30 |
Jacobi Matrices and Central Limit Theorems in Random Matrix Theory |
Room 2 | |
Tuesday 7th April 2015 | |||
---|---|---|---|
09:00 to 09:50 | No Room Required | ||
09:50 to 10:00 | Room 1 | ||
09:50 to 10:00 | Room 1 | ||
09:50 to 10:00 | Room 1 | ||
10:00 to 11:00 | Room 1 | |
|
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
Semi-classical analysis of non-self-adjoint transfer operators |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 | Room 1 | |
|
14:30 to 15:00 | No Room Required | ||
15:00 to 15:25 | Room 1 | |
|
15:30 to 15:55 | Room 1 | |
|
16:00 to 16:25 | Room 1 | |
|
16:30 to 17:30 | No Room Required |
Wednesday 8th April 2015 | |||
---|---|---|---|
10:00 to 11:00 | Room 1 | |
|
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
Recurrent random walks in random and quasi-periodic environments on a strip |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
12:30 to 13:30 | No Room Required | ||
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 |
Spectral Properties of Schroedinger Operator with a Quasi-periodic Potential in Dimension Two |
Room 1 | |
14:30 to 15:00 | No Room Required | ||
15:00 to 16:00 | Room 1 | |
|
16:00 to 16:25 | Room 1 | |
Thursday 9th April 2015 | |||
---|---|---|---|
10:00 to 11:00 | Room 1 | |
|
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 | Room 1 | |
|
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 | Room 1 | |
|
14:30 to 15:00 | No Room Required | ||
15:00 to 15:25 | Room 1 | |
|
15:30 to 15:55 |
Ergodic properties and localization for Delone-Anderson models |
Room 1 | |
16:00 to 16:25 | Room 1 | |
|
19:30 to 22:00 | No Room Required |
Friday 10th April 2015 | |||
---|---|---|---|
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
Level statistics for 1-dimensional Schr\"odinger operator and beta-ensemble |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 | Room 1 | |
|
14:30 to 15:00 | No Room Required | ||
15:00 to 15:25 |
The isospectral torus of quasi-periodic Schrodinger operators via periodic approximations |
Room 1 | |
15:30 to 15:55 |
Spectral packing dimension for 1-dimensional quasiperiodic Schrodinger operators |
Room 1 | |
16:00 to 16:25 | Room 1 | |
|
16:30 to 16:55 |
On the Homogeneity of the Spectrum for Quasi-Periodic Schroedinger Operators |
Room 1 | |
Tuesday 14th April 2015 | |||
---|---|---|---|
14:00 to 16:00 |
A short introduction into multi-particle Anderson localization (a mini-course) |
Room 2 | |
Wednesday 15th April 2015 | |||
---|---|---|---|
15:00 to 16:00 | Room 2 |
Wednesday 22nd April 2015 | |||
---|---|---|---|
14:00 to 16:00 |
A short introduction into multi-particle Anderson localization (a mini-course) |
Room 2 |
Tuesday 28th April 2015 | |||
---|---|---|---|
14:00 to 15:00 |
Non-linear generalisation of the May-Wigner instability transition (joint work with Yan Fyodorov) |
Room 2 | |
15:00 to 16:00 |
Eigenvalues of the Schroedinger operator on infinite combinatorial and quantum graphs |
Room 2 | |
Thursday 30th April 2015 | |||
---|---|---|---|
14:00 to 15:00 | Room 2 |
Friday 1st May 2015 | |||
---|---|---|---|
09:00 to 17:00 | Room 2 | ||
14:45 to 16:00 | Discussion Room |
Thursday 7th May 2015 | |||
---|---|---|---|
13:30 to 14:30 |
Asymptotic behaviour of a sine-kernel determinant in the theory of the log-gas and random matrices |
Room 2 |
Monday 11th May 2015 | |||
---|---|---|---|
16:00 to 17:00 |
Rothschild Distinguished Visiting Fellow Lecture: Disordered systems and related spectra |
Room 1 | |
17:00 to 18:00 | No Room Required |
Tuesday 12th May 2015 | |||
---|---|---|---|
14:00 to 16:00 | Discussion Room |
Wednesday 13th May 2015 | |||
---|---|---|---|
14:00 to 15:00 |
Conductance and absolutely continuous spectrum of 1D samples |
Room 2 | |
15:15 to 16:00 |
How to Place an Obstacle so as to Optimize the Dirichlet Eigenvalues in $\R^2$. |
Room 2 | |
Wednesday 27th May 2015 | |||
---|---|---|---|
14:00 to 15:00 |
Density of states and Lyapunov exponent in the heavy tail potentials |
Room 2 | |
15:00 to 16:30 | Discussion Room |
Tuesday 2nd June 2015 | |||
---|---|---|---|
13:00 to 17:00 | Discussion Room |
Wednesday 3rd June 2015 | |||
---|---|---|---|
14:00 to 15:00 |
Derivation of the Fick's law for the Lorentz model in a low density regime |
Room 2 | |
15:10 to 16:10 | Room 2 | |
Wednesday 10th June 2015 | |||
---|---|---|---|
14:00 to 15:00 | Room 2 | |
|
15:10 to 16:10 |
Anderson localization in a multi-dimensional deterministic disorder I |
Room 2 | |
Thursday 11th June 2015 | |||
---|---|---|---|
14:00 to 15:00 |
Compactness principles and convergence of spectra in double-porosity models |
Room 2 | |
15:10 to 16:10 |
Homogenization of operators with quasi-periodic coefficients |
Room 2 | |
Friday 12th June 2015 | |||
---|---|---|---|
14:00 to 15:00 |
Anderson localization in a multi-dimensional deterministic disorder II |
Room 2 | |
Monday 15th June 2015 | |||
---|---|---|---|
14:00 to 17:00 | Discussion Room |
Tuesday 16th June 2015 | |||
---|---|---|---|
14:00 to 15:00 |
Absolute continuity returns: potentials that are periodic in some directions only |
Room 2 | |
Monday 22nd June 2015 | |||
---|---|---|---|
09:00 to 09:50 | No Room Required | ||
09:50 to 10:00 | No Room Required | ||
10:00 to 11:00 | Room 1 | |
|
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
On the two-dimensional random walk in an isotropic random environment |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 |
From the mesoscopic to microscopic scale in random matrix theory |
Room 1 | |
14:30 to 15:00 | No Room Required | ||
15:00 to 16:00 | Room 1 | |
|
16:00 to 17:00 | Room 1 | |
|
17:00 to 18:00 | No Room Required |
Wednesday 24th June 2015 | |||
---|---|---|---|
10:00 to 11:00 |
Pure point spectrum in the regime of zero Lyapunov exponents |
Room 1 | |
11:00 to 11:30 | No Room Required | ||
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 |
Behavior of the spectrum of the periodic Schrodinger operators near the edges of the gaps |
Room 1 | |
14:30 to 15:00 | No Room Required | ||
15:00 to 16:00 |
$L_1$-Estimates for Eigenfunctions of the Dirichlet Laplacian |
Room 1 | |
19:30 to 22:00 |
Conference Dinner at Cambridge Union Society hosted by Cambridge Dining Co. |
No Room Required |
Thursday 25th June 2015 | |||
---|---|---|---|
10:00 to 11:00 | Room 1 | |
|
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 | Room 1 | |
|
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 | Room 1 | |
|
14:30 to 15:00 | No Room Required | ||
15:00 to 16:00 | Room 1 | |
|
16:00 to 17:00 |
Green's function asymptotic behavior near a non-degenerate spectral edge of a periodic operator |
Room 1 | |
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