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


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5th January 2015 to 16th January 2015

Organisers: David Damanik (Rice University), Alexander Sobolev (University College London) and Leonid Parnovski (University College London)

Workshop Theme

The winter school "Periodic, Almost-periodic, and Random Operators" opens the 6 month programme "Periodic and Ergodic Spectral Problems". The aim of this winter school is to offer several mini-courses which will serve as an introduction to the subject matter of the semester programme. These mini-courses will present background information and an overview of the most important results and open questions in the areas of periodic, almost periodic, and random operators. The school is aimed at an audience primarily consisting of graduate students and recent Ph. D. recipients. Attending these mini-courses will allow the participants to get a general feeling for the area and it will facilitate interactions with the experts that are present at the institute during the winter school and/or later parts of the programme period. It will also make the talks in the three subsequent workshops and various working groups more accessible to the junior participants.

There has been exciting recent progress in the area of the school on several fronts. For example:
  • for periodic operators, a proof of the Bethe-Sommerfeld Conjecture, stating that the number of gaps of the spectrum of multidimensional periodic Schrodinger operators is finite;
  • for periodic and almost periodic operators, the complete asymptotic expansions of the integrated density of states;
  • for quasi-periodic operators, Avila's global theory, characterizing in the one-dimensional one-frequency analytic case the typical spectral type via the corresponding cocycle behaviour;
  • for random operators, a localization proof in the multi-dimensional continuous case for all single-site distributions;
  • for random operators, a study of the transition between the delocalized region and the localized region on the Bethe lattice.

The mini-courses presented at the school will start from discussing basic material and giving an introduction to each of the three sub-areas (periodic, almost periodic, and random) and conclude by presenting at least some of the results mentioned above. We plan to have eight mini-courses, each consisting of seven or eight lectures.

The anticipated mini-course speakers and the topics of their courses will be:
  • David Damanik (General spectral properties of ergodic operators)
  • Abel Klein (Random operators: multiscale analysis)
  • Frederic Klopp (Random operators: many body problems)
  • Peter Kuchment (Introduction to periodic operators)
  • Christoph Marx (One-dimensional quasi-periodic Schrödinger operators)
  • Barry Simon (Orthogonal polynomials)
  • Alexander Sobolev (Periodic operators: the method of gauge transform)

The mini-courses therefore will address all three sub-areas. By presenting them in a unified setting, we hope that this will lead to an improved understanding of the connections between them and possibly also to new collaborations.

Deadline for applications: 28th September 2014

Apply now



Registration Only
  • Registration Package: £455
  • Student Registration Package: £300

The Registration Package includes admission to all seminars, lunches and refreshments on the days that lectures take place (Monday - Friday), wine reception and formal dinner, but does not include other meals or accommodation.

Formal Dinner Only
  • Formal dinner: £40

Participants on the Registration Package, including organisers and speakers, are automatically included in this event. For all remaining participants who would like to attend, such as Visiting Fellows, programme participants or their guests, the above charge will apply.


Unfortunately we do not have any accommodation to offer so all successful applicants will need to source their own accommodation. Please see the Hotels Combined website for a list of local hotels and guesthouses.



Lunch will be served at Wolfson Court in the Cafeteria from 12:30 to 13:30 on days that lectures take place.

  • Accommodation Package and Registration Package participants should present their badge as payment for their meal
  • Those issued with a blue Institute door entrance card can add money onto the card via the Porters' Lodge at Wolfson Court
  • Other participants must purchase their meal using their dining card via the Porters' Lodge (forms can be found on the registration desk or at the Porters' Lodge)

Evening Meal

Participants are free to make their own arrangements for dinner.

Formal Dinner

The Formal Dinner will take place at 19:30 on Wednesday 7 January 2015 at Emmanuel College. Participants on the Registration Package, including organisers and speakers, are automatically included in this event. All remaining participants are encouraged to attend at a charge (price £40).

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