Periodic and ergodic spectral problems

Programme theme

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 R^d or Z^d; 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

Preprints

Title	Year	Programme
Killip-Simon problem and Jacobi flow on GSMP matrices Authors: Peter Yuditskii Download PDF	2014	PEP	21 October 2016
Generalized linear Boltzmann equations for particle transport in polycrystals Authors: J Marklof, A Strombergsson Download PDF	2014	PEP	21 October 2016
Quadratic Weyl sums, automorphic functions, and invariance principles Authors: F Cellarosi, J Marklof Download PDF	2014	PEP	21 October 2016
Spectral honogeneity of limit-periodic Schrödinger operators Authors: Jake Fillman, M Lukic Download PDF	2014	PEP	21 October 2016
Generalized Prüfer variables for perturbations of Jacobi and CMV matrices Authors: M Lukic, DC Ong Download PDF	2014	PEP	21 October 2016
Fractional Brownian motion with Hurst index H=0 and the Gaussian Unitary Ensemble Authors: YV Fyodorov, Boris Khoruzhenko, NJ Simm Download PDF	2014	PEP	21 October 2016
Accumulation of complex eigenvalues of an indefinite Sturm-Liouville operator with a shifted Coulomb potential Authors: M Levitin, Marcello Seri Download PDF	2014	PEP	21 October 2016
From constant to non-degenerately vanishing magnetic fields in superconductivity Authors: B Helffer, A Kachmar Download PDF	2014	PEP	21 October 2016
Mixed spectral regimes for square Fibonacci Hamiltonians Authors: Jake Fillman, Y Takahash, W Yessen Download PDF	2014	PEP	21 October 2016
Chamber's forumla for the graphene and the Hou model with kagome periodicity and applications Authors: B Helffer, P Kerdelhue, J Royo-Letelier Download PDF	2014	PEP	21 October 2016
Exponential scaling limit of the single-particle Anderson model via adaptive feedback scaling Authors: V Chulaevsky Download PDF	2014	PEP	21 October 2016
Efficient localization bounds in a continuous N-particle Anderson model with long-range interaction Authors: V Chulaevsky Download PDF	2014	PEP	21 October 2016
Asymptotics for Erd?s-Solojev zero modes in strong fields Authors: Daniel Mark Elton Download PDF	2014	PEP	21 October 2016
Mixed spectral types for one frequency discrete quasi-periodic Schrödinger operator Authors: S Zhang Download PDF	2014	PEP	21 October 2016
$\it L$$^2$-Reducibility and localization for quasiperiodic operators Authors: S Jitomirskaya, Ilya Kachkovskiy Download PDF	2014	PEP	21 October 2016
A uniform area law for the entanglement of eigenstates in the disordered XY chain Authors: H Abdul-rahman, Gunter Stolz Download PDF	2014	PEP	21 October 2016
Magnetic wells in dimension three Authors: B Helffer, Y Kordyukov, N Raymond, S Vu Ngoc Download PDF	2014	PEP	21 October 2016
Mixed normal-superconducting states in the presence of strong electric currents Authors: Y Almog, B Helffer, XB Pan Download PDF	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 Download PDF	2014	PEP	21 October 2016
On transport properties of isotropic quasiperiodic $\it XY$ spin chains Authors: Ilya Kachkovskiy Download PDF	2014	PEP	21 October 2016
Complete exponential localization in a discrete multi-particle Anderson model with interaction of infinite range Authors: V Chulaevsky Download PDF	2014	PEP	21 October 2016
Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel Authors: Christian Sadel Download PDF	2014	PEP	21 October 2016
Invariance principle for the periodic Lorentz gas in the Boltzmann-Grad limit Authors: J Marklof, B Toth Download PDF	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 Download PDF	2014	PEP	21 October 2016
On the phase-space distribution of Bloch eigenmodes for periodic point scatterers Authors: J Griffin Download PDF	2014	PEP	21 October 2016
Exponential Riemann sums and "near" -quasicrystals Authors: Toshikazu Sunada Download PDF	2014	PEP	21 October 2016
Ballistic transport for the Schrödinger operator with limit-periodic or quasi-periodic potential in dimension two Authors: Yulia Karpeshina, Young-Ran Lee, Roman Shterenberg, Gunter Stolz Download PDF	2014	PEP	21 October 2016
Localization principle for compact Hankel operators Authors: A Pushnitski, Dimitri Yafaev Download PDF	2014	PEP	21 October 2016
Homogenization of nonstationary Schrödinger type equations with periodic coefficients Authors: Tatiana Suslina Download PDF	2014	PEP	21 October 2016
Two-scale series expansions for travelling wave packets in one-dimensional periodic media Authors: KD Cherednichenko Download PDF	2014	PEP	21 October 2016
A sub-Riemannian Santaló formula with applications to isoperimetric inequalities and Dirichlet spectral gap of hypoelliptic operators Authors: D Prandi, L Rizzi, Marcello Seri Download PDF	2014	PEP	21 October 2016
An overview of periodic elliptic operators Authors: Peter Kuchment Download PDF	2014	PEP	21 October 2016
On the structure of band edges of 2D periodic elliptic operators Authors: Nikolai Filonov, Ilya Kachkovskiy Download PDF	2014	PEP	21 October 2016
Best rational approximation of functions with logarithmic singularities Authors: A Pushnitski, Dimitri Yafaev Download PDF	2014	PEP	21 October 2016
Almost periodicity in time of solutions of the KDV equation Authors: I Binder, David Damanik, Michael Goldstein, M Lukic Download PDF	2014	PEP	21 October 2016
Limit-Periodic continuum Schödinger operators with zero measure Cantor spectrum Authors: David Damanik, Jake Fillman, M Lukic Download PDF	2014	PEP	21 October 2016
Characterization of the metal-insulator transport transition for the two-particle Anderson model Authors: A Klein, ST Nguyen, C Rojas-molina Download PDF	2014	PEP	21 October 2016

Workshops

PEPW01

Seminars

Sunday 9th February 2014
14:00 to 15:00	The Point Scatterer: A Survey	Room 1

Monday 5th January 2015
09:00 to 09:55	Registration	No Room Required
09:55 to 10:00	Welcome from John Toland (INI Director)	No Room Required
10:00 to 11:00	General spectral properties of ergodic operators I	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Introduction to periodic operators I	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	Introduction to periodic operators II	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 16:00	Random operators: multiscale analysis I	Room 1
16:00 to 17:00	Random operators: multiscale analysis II	Room 1
17:00 to 18:00	Welcome Wine Reception	No Room Required

Tuesday 6th January 2015
09:00 to 10:00	Orthogonal polynomials I	Room 1
10:00 to 11:00	Orthogonal polynomials II	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	General spectral properties of ergodic operators II	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	General spectral properties of ergodic operators III	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 16:00	Introduction to periodic operators III	Room 1
16:00 to 17:00	Introduction to periodic operators IV	Room 1

Wednesday 7th January 2015
09:00 to 10:00	General spectral properties of ergodic operators IV	Room 1
10:00 to 11:00	Orthogonal polynomials III	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Orthogonal polynomials IV	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	Random operators: multiscale analysis III	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 16:00	Random operators: multiscale analysis IV	Room 1
16:00 to 17:00	Introduction to periodic operators V	Room 1
19:30 to 22:00	Conference Dinner at Emmanuel College	No Room Required

Thursday 8th January 2015
09:00 to 10:00	Random operators: many body problems I	Room 1
10:00 to 11:00	Random operators: many body problems II	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Random operators: many body problems III	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	Random operators: multiscale analysis V	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 16:00	Random operators: multiscale analysis VI	Room 1
16:00 to 17:00	Introduction to periodic operators VI	Room 1

Friday 9th January 2015
09:00 to 10:00	Random operators: many body problems IV	Room 1
10:00 to 11:00	Random operators: many body problems V	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Random operators: many body problems VI	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	Periodic operators: the method of gauge transform I	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 16:00	Random operators: multiscale analysis VII	Room 1
16:00 to 17:00	Random operators: multiscale analysis VIII	Room 1

Monday 12th January 2015
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	Periodic operators: the method of gauge transform II	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 16:00	Periodic operators: the method of gauge transform III	Room 1
16:00 to 17:00	Periodic operators: the method of gauge transform IV	Room 1
17:00 to 18:30	Tales of Our Forefathers	Room 1
18:30 to 19:30	Wine Reception	No Room Required

Tuesday 13th January 2015
09:00 to 10:00	Orthogonal polynomials V	Room 1
10:00 to 11:00	Orthogonal polynomials VI	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	One-dimensional quasi-periodic Schrödinger operators I	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
13:00 to 17:00	Informal discussion (D Monaco)	Discussion Room

Wednesday 14th January 2015
11:30 to 12:30	Killip-Simon problem and Jacobi flow on GSMP matrices	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	Orthogonal polynomials VII	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 16:00	Orthogonal polynomials VIII	Room 1
16:00 to 17:00	One-dimensional quasi-periodic Schrödinger operators II	Room 1

Thursday 15th January 2015
09:00 to 10:00	Periodic operators: the method of gauge transform V	Room 1
10:00 to 11:00	Periodic operators: the method of gauge transform VI	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	One-dimensional quasi-periodic Schrödinger operators III	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
13:30 to 17:00	informal discussion	Discussion Room

Friday 16th January 2015
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	One-dimensional quasi-periodic Schrödinger operators IV	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 16:00	One-dimensional quasi-periodic Schrödinger operators V	Room 1
16:00 to 17:00	One-dimensional quasi-periodic Schrödinger operators VI	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

Monday 9th February 2015
14:00 to 15:00	The point scatterer: a survey	Room 1

Wednesday 11th February 2015
14:00 to 15:00	Schrodinger or Pauli operators with self-generated magnetic fields	Room 1

Tuesday 17th February 2015
14:00 to 15:00	Entanglement entropy of free fermions	Room 2

Wednesday 18th February 2015
14:00 to 15:00	Exponential dynamical localization in N-particle Anderson models on graphs with long-range interaction via Fractional Moment Analysis	Room 2

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

Tuesday 10th March 2015
14:00 to 15:00	The string density problem and the Camassa-Holm equation	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

Thursday 19th March 2015
12:30 to 13:30	Some results on $d \times d$ cocycles	Room 2

Monday 23rd March 2015
09:00 to 09:50	Registration	No Room Required
09:50 to 10:00	Welcome from John Toland (INI Director)	Room 1
10:00 to 11:00	Index theory on end-periodic manifolds	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Uncertainty relations and Wegner estimates for random breather potentials	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	A Wegner estimate and localisation for alloy-type models with sign-changing exponentially decaying single-site potentials	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 16:00	Spectral asymptotics of Zahkarov Shabat operators and their application to the nonlinear Schrödinger equation on the circle	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	Welcome Wine Reception	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	Morning Coffee	No Room Required
11:30 to 12:30	Anderson localization for one-dimensional ergodic Schrödinger operators with piecewise monotonic sampling functions	Room 1
12:30 to 13:30	Lunch at Wolfson Court	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	Afternoon Tea	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	On Level Spacings for Jacobi Operators	Room 1

Wednesday 25th March 2015
09:00 to 17:00	Day dedicated to the memory of B.M. Levitan	No Room Required
10:00 to 11:00	Surface waves and scattering by unbounded obstacles	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:00 to 11:30	Morning Coffee	No Room Required
11:00 to 11:30	Morning Coffee	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	Lunch at Wolfson Court	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	Afternoon Tea	No Room Required
15:00 to 16:00	Periodic spectral problem for the massless Dirac operator	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	Kinetic transport in crystals and quasicrystals	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:00 to 11:30	Morning Coffee	No Room Required
11:00 to 11:30	Morning Coffee	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	Lunch at Wolfson Court	No Room Required
19:30 to 22:00	Conference Dinner at Christ's College	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	Morning Coffee	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	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	Everywhere discontinuous anisotropy of thin periodic composite plates	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 16:00	Maryland equation, renormalization formulas and mimimal meromorphic solutions to difference equations	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

Thursday 2nd April 2015
12:30 to 13:30	Continuity of Lyapunov Exponents via Large Deviations	Room 2

Tuesday 7th April 2015
09:00 to 09:50	Registration	No Room Required
09:50 to 10:00	Welcome from John Toland (INI Director)	Room 1
09:50 to 10:00	Welcome from John Toland (INI Director)	Room 1
09:50 to 10:00	Welcome from John Toland (INI Director)	Room 1
10:00 to 11:00	Dry Ten Martini Problem in Non-Critical Case	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Semi-classical analysis of non-self-adjoint transfer operators	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	Phase transitions for the almost Mathieu operator	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 15:25	Lyapunov exponents of quasi-periodic cocycles	Room 1
15:30 to 15:55	Arithmetic Spectral Transitions for the Maryland Model	Room 1
16:00 to 16:25	Measure of the spectrum of the extended Harper's model	Room 1
16:30 to 17:30	Welcome Wine Reception	No Room Required

Wednesday 8th April 2015
10:00 to 11:00	Dynamics of two quasi-periodically perturbed systems	Room 1
11:00 to 11:30	Morning Coffee	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	Lunch at Wolfson Court	No Room Required
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
12:30 to 13:30	Lunch at Wolfson Court	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	Afternoon Tea	No Room Required
15:00 to 16:00	Continuity of Lyapunov Exponents and Cantor spectrum for a class of $C^2$ Quasiperiodic Schr\"odinger Cocycles	Room 1
16:00 to 16:25	High energy asymptotics of the integrated density of states of almost periodic pseudo-differential operators	Room 1

Thursday 9th April 2015
10:00 to 11:00	Microlocal properties of scattering matrices	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Wegner estimates for deformed Gaussian ensembles	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	On gaps and bands of quasi-periodic operators	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 15:25	Random nonmonotonic multichannel Schr\"{o}dinger operators	Room 1
15:30 to 15:55	Ergodic properties and localization for Delone-Anderson models	Room 1
16:00 to 16:25	Anderson transition at 2D growth-rate for the Anderson model on antitrees with normalized edge weights	Room 1
19:30 to 22:00	Conference Dinner at Gonville and Caius College	No Room Required

Friday 10th April 2015
11:00 to 11:30	Morning Coffee	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	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	The Fibonacci Hamiltonian	Room 1
14:30 to 15:00	Afternoon Tea	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	Homogeneous Spectrum for Limit-Periodic Operators	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	On the Generic Cantor Spectrum problem	Room 2

Wednesday 22nd April 2015
14:00 to 16:00	A short introduction into multi-particle Anderson localization (a mini-course)	Room 2

Thursday 23rd April 2015
14:00 to 15:00	Spectra of Sample Auto-Covariance Matrices	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	PEP Discussion Group (no recording required)	Room 2

Friday 1st May 2015
09:00 to 17:00	PEP Discussion Group (no recording required)	Room 2
14:45 to 16:00	Informal discussion	Discussion Room

Wednesday 6th May 2015
13:30 to 14:30	Magnetic wells in dimension two and three	Room 2

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	Wine Reception after Rothschild Lecture	No Room Required

Tuesday 12th May 2015
14:00 to 16:00	informal discussion	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 20th May 2015
11:30 to 12:30	Dissipative Transport in the Localization Regime	Room 1
14:00 to 15:00	Jacobi Matrices and Non-equilibrium Statistical Mechanics	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	booked by Leonid (PEP organiser)	Discussion Room

Tuesday 2nd June 2015
13:00 to 17:00	Leonid Parnovski (DIscussion)	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	Uniqueness of the Leray-Hopf solution for a dyadic model	Room 2

Thursday 4th June 2015
14:00 to 15:00	Stark-Wannier ladders and cubic exponential sums	Room 2

Wednesday 10th June 2015
14:00 to 15:00	The nodal count mystery	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	Informal discussion	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	Registration	No Room Required
09:50 to 10:00	Welcome from Christie Marr (INI Deputy Director)	No Room Required
10:00 to 11:00	On non-smooth functions of Wiener-Hopf operators	Room 1
11:00 to 11:30	Morning Coffee	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	Lunch at Wolfson Court	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	Afternoon Tea	No Room Required
15:00 to 16:00	On fluctuations of eigenvalues of random band matrices	Room 1
16:00 to 17:00	Primitive Pythagorean triples and "near" quasicrystals	Room 1
17:00 to 18:00	Welcome Wine Reception	No Room Required

Tuesday 23rd June 2015
10:00 to 11:00	An eigensystem approach to Anderson localization	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	An eigensystem approach to Anderson localization, part II	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	Dissipative transport in the localized regime	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 16:00	New properties of entropy and their consequences	Room 1
16:00 to 17:00	Level Spacing for Non-Monotone Anderson Models	Room 1

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	Morning Coffee	No Room Required
12:30 to 13:30	Lunch at Wolfson Court	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	Afternoon Tea	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	Spectral theory of the Schr?dinger operators on fractals	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Eigenvalue statistics for random Schrodinger operators	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required
13:30 to 14:30	Localisation and ageing in the parabolic Anderson model	Room 1
14:30 to 15:00	Afternoon Tea	No Room Required
15:00 to 16:00	The invariant measure for random walks on a strip	Room 1
16:00 to 17:00	Green's function asymptotic behavior near a non-degenerate spectral edge of a periodic operator	Room 1

Friday 26th June 2015
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Interacting quantum particles in a 1 D random background	Room 1
12:30 to 13:30	Lunch at Wolfson Court	No Room Required

Organisers

David Damanik Rice University
Svetlana Jitomirskaya University of California, Irvine
Frédéric Klopp Université Pierre et Marie Curie Paris
Leonid Parnovski University College London
Alex Sobolev University College London

Periodic and ergodic spectral problems

Programme theme

Preprints

Killip-Simon problem and Jacobi flow on GSMP matrices

Generalized linear Boltzmann equations for particle transport in polycrystals

Quadratic Weyl sums, automorphic functions, and invariance principles

Spectral honogeneity of limit-periodic Schrödinger operators

Generalized Prüfer variables for perturbations of Jacobi and CMV matrices

Fractional Brownian motion with Hurst index H=0 and the Gaussian Unitary Ensemble

Accumulation of complex eigenvalues of an indefinite Sturm-Liouville operator with a shifted Coulomb potential

From constant to non-degenerately vanishing magnetic fields in superconductivity

Mixed spectral regimes for square Fibonacci Hamiltonians

Chamber's forumla for the graphene and the Hou model with kagome periodicity and applications

Exponential scaling limit of the single-particle Anderson model via adaptive feedback scaling

Efficient localization bounds in a continuous N-particle Anderson model with long-range interaction

Asymptotics for Erd?s-Solojev zero modes in strong fields

Mixed spectral types for one frequency discrete quasi-periodic Schrödinger operator

$\it L$$^2$-Reducibility and localization for quasiperiodic operators

A uniform area law for the entanglement of eigenstates in the disordered XY chain

Magnetic wells in dimension three

Mixed normal-superconducting states in the presence of strong electric currents

Lower bound for the number of critical points of minimal spectral $\it k$-partitions for $\it k$ large.

On transport properties of isotropic quasiperiodic $\it XY$ spin chains

Complete exponential localization in a discrete multi-particle Anderson model with interaction of infinite range

Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel

Invariance principle for the periodic Lorentz gas in the Boltzmann-Grad limit

Green's function asymptotics near the internal edges of spectra of periodic elliptic operators: spectral gap interior.

On the phase-space distribution of Bloch eigenmodes for periodic point scatterers

Exponential Riemann sums and "near" -quasicrystals

Ballistic transport for the Schrödinger operator with limit-periodic or quasi-periodic potential in dimension two

Localization principle for compact Hankel operators

Homogenization of nonstationary Schrödinger type equations with periodic coefficients

Two-scale series expansions for travelling wave packets in one-dimensional periodic media

A sub-Riemannian Santaló formula with applications to isoperimetric inequalities and Dirichlet spectral gap of hypoelliptic operators

An overview of periodic elliptic operators

On the structure of band edges of 2D periodic elliptic operators

Best rational approximation of functions with logarithmic singularities

Almost periodicity in time of solutions of the KDV equation

Limit-Periodic continuum Schödinger operators with zero measure Cantor spectrum

Characterization of the metal-insulator transport transition for the two-particle Anderson model

Workshops

Periodic, almost-periodic, and random operators: instructional school

Periodic and other ergodic problems

Almost-periodic and other ergodic problems

Random and other ergodic problems

Seminars

Organisers

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