Title: Spectral Theory of Orthogonal Polynomials
2013.09.10 |
| Date | Mon 17 Feb — Thu 20 Feb |
| Time | 09:00 — 16:00 |
| Location | QGM |
Abstract
Spectral theory is the study of the connections between the fundamental equations of a system and its spectral properties - typically as seen in audio, optical or other scattering data. The difficulty is often that there is no explicit solution of the inverse problem - that is going from the spectral data to the parameters of the equations ("can you hear the shape of a drum"). The spectral theory of orthogonal polynomials on the real line (OPRL) or unit circle (OPUC) is an especially useful spectral theory laboratory precisely because the solution of the inverse problem is so explicit. These lectures will begin by describing the underlying framework, then turn to the basic results for the case of a single interval or whole circle (regularity, Rachmanov’s theorem, Szego’s theorem, Killip-Simon theorem) and then discuss the finite gap case which requires the study of certain Fuchsian groups. No prior exposure to OPs or Fuchsian groups will be required but the students will be expected to have a working knowledge of the basics of functional analysis and Hilbert space operator theory, especially of the spectral theorem.
Guest speakers
Andrei Martínez Finkelshtein (Universidad de Almería)
Jacob Stordal Christiansen (Lund University)
Jonathan Breuer (Hebrew University of Jerusalem)
Program
Monday (Physics Aud.: 1523-318)
09:30 - 10:00 Coffee/tea
10:00 - 10:45 Introduction and Overview by Barry Simon (download slides (1))
11:15 - 12:00 Szego's Theorem for OPUC by Barry Simon (download slides (2))
12:00 - 14:00 Lunch
14:15 - 15:00 Three Kinds of Polynomial Asymptotics, I by Barry Simon (download slides (3/4))
15:00 - 15:15 Coffee break
15:15 - 16:00 Three Kinds of Polynomial Asympotics, II by Barry Simon (download slides (3/4))
18:00 Networking dinner (MatLab)
Tuesday (Aud. F: 1534-125)
09:30 - 10:00 Coffee/tea
10:00 - 10:45 Killip-Simon Theorem on [-2,2] by Barry Simon (download slides (5))
11:15 - 12:00 Szego Asymptotics and Shohat-Nevai for [-2; 2] by Barry Simon (download slides (6))
12:00 - 14:00 Lunch
14:00 - 14:45 Periodic OPRL by Barry Simon (download slides (7))
14:45 - 15:15 Coffee break
15:15 - 16:00 Finite Gap Isospectral Torus by Barry Simon (download slides (8))
Wednesday
09:30 - 10:00 Coffee/tea
10:00 - 10:45 Fuchsian Groups and Finite Gaps, I by Barry Simon (Aud. G2: 1532-122), (download slides (9))
11:15 - 12:00 Fuchsian Groups and Finite Gaps, II by Barry Simon (Aud. G2: 1532-122)., (download slides (10))
12:00 - 14:00 Lunch
14:00 - 14:45 Orthogonal polynomials in random matrix models and non-intersecting paths by Andrei Martínez Finkelshtein (Aud. D1: 1531-113) - (download slides)
14:45 - 15:15 Coffee break
15:15 - 16:15 Colloquium by Barry Simon (Aud. D1: 1531-113)
18:00 Special Dinner
Thursday (Aud. D1: 1531-113)
09:30 - 10:00 Coffee/tea
10:00 - 10:45 Selected Additional Topics, I by Barry Simon (download slides (11/12))
11:15 - 12:00 Selected Additional Topics, II by Barry Simon (download slides (11/12))
12:00 - 14:00 Lunch
14:00 - 14:45 Infinite gap Jacobi matrices by Jacob Stordal Christiansen (download slides)
14:45 - 15:15 Coffee break
15:15 - 16:00 Spectral theory and orthogonal polynomial ensembles by Jonathan Breuer (download slides)
Social programme
Included in the event
In special cases, QGM is able to offer limited financial support to junior researchers (PhD students and postdocs). Only applications received before 10 Jan 2014 will be considered for financial support.
Participants
Andersen, Jørgen Ellegaard (Aarhus University - Organizer)
Andersen, Troels Bak (Aarhus University)
Attia, Mohamed Jalel (Faculty of sciences of Gabes)
Bech, Mads (Aarhus University)
Borrego Morell, Jorge Alberto (Universidade Estadual Paulista)
Castillo, Kenier (Universidade Estadual Paulista)
Cornean, Horia (Aalborg University)
Crowdy, Darren (Imperial College London)
Erb, Wolfgang (University of Lübeck)
Egsgaard, Jens Kristian (Aarhus University)
Eichinger, Benjamin (Institute of Analysis, Johannes Kepler University Linz)
Eliaz, Latif (The Hebrew University of Jerusalem)
Fahs, Benjamin (Université catholique de Louvain)
Fedosova, Ksenia (University of Bonn)
Ferrigo, Marco (University of Pisa)
Fillman, Jacob (Rice University)
Fischbacher, Christoph (University of Kent)
Fournais, Søren (Aarhus University)
Frandsen, Eva Gjaldbæk (Aarhus University)
Gammelgaard, Niels Leth (Aarhus University)
Garza, Lino (Universidad Carlos III de Madrid)
Grzegorz, ?widerski (University of Wroc?aw)
Hein, Morten Tiljeset (Aarhus University)
Herbig, Hans-Christian (Charles University Prague)
Hynek, Mariusz (KTH Sweden)
Jex, Michal (Faculty of Nuclear Sciences and Physical Engineering, CTU in Prague)
Koellner, Jan (IADM, University of Stuttgart)
Komlov, Alexander (Steklov Mathematical Institute)
Kozhan, Rostyslav (Royal Institute of Technology (KTH), Stockholm)
Krueger, Torben (LMU Munich / IST Austria)
Kozlowska, Katarzyna (University of Reading)
Lambert, Gaultier (KTH Sweden)
Marberg, Eric, (Stanford University)
Marchukov, Oleksandr (Aarhus University)
Munger, Paul (Rice University)
Nissen, Jens-Jakob Kratmann (Aarhus University)
Novak, Radek (Faculty of Nuclear Sciences and Physical Engineering, CTU in Prague)
Pacheco, Carlos G. (CINVESTAV-IPN, Mexico)
Penko, Sebastian (University of Lübeck)
Rasmussen, Moten Grud (Aalborg University)
Ruszkowski, Bartosch (University of Stuttgart)
Sajjad, Sajjad (Swansea University)
Schach, Jacob (Aarhus University)
Schimmer, Lukas (Imperial College London)
Schmidt, Thomas (Aarhus University)
Seyyedkheili, Javad Golipour (IPM, Iran)
Shayanfar, Nikta (K.N.Toosi University of Technology)
Sikander, Shehryar (Aarhus University)
Symons, Freddy (Cardiff University)
Thabet, Faouzi (University of Gabes)
Tiljeset, Morten Hein (Aarhus University)
Volosniev, Artem (Aarhus University)
Waqquas, Sarah (University of Edinburgh)
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Visitor information
Group picture, 20 Feb. 2014
