SCIENTIFIC PROGRAMS AND ACTIVITIES

December 19, 2014

July 25-29,2011
Conference on Blaschke Products and their Applications
Hosted by the Fields Institute, held at the University of Toronto
Bahen Building(BA1200)map

Organizers: Javad Mashreghi (Laval, Canada),
Emmanuel Fricain (Lyon I, France

OVERVIEW
Infinite Blaschke products were introduced by Blaschke in 1915. However, finite Blaschke products, as a subclass of rational functions, has existed long before without being specifically addressed as finite Blaschke products. In 1929, R. Nevanlinna introduced the class of bounded analytic functions with almost everywhere unimodular boundary values. Then the term inner function was coined much later by A. Beurling in his seminal study of the invariant subspaces of the shift operator.

The first extensive study of the properties of inner functions was made by Frostman, Seidel and F. Riesz. The Riesz technique in extracting the zeros of a function in a Hardy space is considered as the first step of the full canonical factorization of such elements. The disposition of zeros of an inner function is intimately connected with the existence of radial limits of the inner function and its derivatives.

For almost a century Blaschke products have been studied and exploited by mathematicians. Their boundary behaviour, the asymptotic growth of various integral means of Blaschke products and their derivatives, their applications in several branches of mathematics in particular as solutions to extremal problems, their membership in different function spaces and their dynamics are examples from a long list of active research domains in which they show their face.

In this conference, prominent mathematicians from around the world will gather to talk about these beautiful creatures and their application in other domains.

Schedule

Monday, July 25 (Bahen Centre Room 1200) map
Chair: William Ross (AM), Artur Nicolau (PM)
8:00-8:20 On-site Registration & Morning Coffee
8:20-8:30 Welcome & Introduction
8:30-9:30 Pamela Gorkin (Bucknell University)
To get (or not to get) uniform approximation by interpolating Blaschke products
9:30-10:30 Laurent Baratchart (INRIA)
Rational approximation and Morse theory
10:30-10:50 Coffee Break
10:50-11:50 Joseph Cima (University of North Carolina)
A survey of recent results on TTO's
11:50-14:00 Lunch Break
14:00-15:00 Ulrich Daepp (Bucknell University)
Geometric Properties of Finite Blaschke Products
15:00-16:00 Eugene Shargorodsky (King's College)
Applications of Blaschke products to the spectral theory of Toeplitz operators
16:00-16:20 Coffee Break
16:20-17:20 Line Baribeau (Laval University)
Hyperbolic divided differences
17:20-18:20 Reception (Fields Institute Atrium, 222 College St.) Cash Bar
Tuesday, July 26 (Bahen Centre Room 1200) map
Chair: Laurent Baratchart (AM), Eugene Shargorodsky (PM)
8:00-8:30 Morning Coffee
8:30-9:30 William Ross (University of Richmond)
Boundary values of functions in the range of a truncated Toeplitz operator
9:30-10:30 Jie Xiao (Memorial University of Newfoundland)
Isoperimetry for Green's Function and Torsional Rigidity over Riemannian Surfaces
10:30-10:50 Coffee Break
10:50-11:50 Artur Nicolau (Universitat Autònoma de Barcelona)
Paths of Inner Functions
11:50-14:00 Lunch Break
14:00-15:00 Daniela Kraus (University of Wuerzburg)
Critical sets of bounded analytic functions, zero sets of Bergman spaces and nonpositive curvature
15:00-16:00 Oliver Roth (University of Würzburg)
Properties of maximal conformal metrics and their developing maps
16:00-16:20 Coffee Break
16:20-17:20 Margit Pap (University of Vienna)
Application of the Blaschke products in Harmonic Analysis
Wednesday, July 27 (Bahen Centre Room 1200) map
Chair: Oliver Roth (AM), Richard Fournier (PM)
8:00-8:30 Morning Coffee
8:30-9:30 Janne Heittokangas (University of Joensuu)
On Blaschke-Oscillatory Differential Equations
9:30-10:30 Richard Fournier (Université de Montréal)
On two problems involving finite Blaschke products
10:30-10:50 Coffee Break
10:50-11:50 Wlodzimierz Zwonek (Jagiellonian University)
Pluripolar extension of Blaschke products
11:50-14:00 Lunch Break
14:00-15:00 Sergei Favorov (Kharkov Naeional University)
Blaschke-type conditions for analytic functions in the unit circle and critical points of Blaschke products
15:00-16:00 Qazi Ibadur Rahman (Université de Montréal)
Local behaviour of entire functions of exponential type
16:00-16:20 Coffee Break
16:20-16:50 Mohammed A. Qazi (Tuskegee University)
An inequality for functions belonging to the Paley-Wiener space
16:50-17:20 Driss Drissi (Kuwait University)
Invariant subspaces for some sequences operator algebras
17:20-17:50 Jamal Benbourenane (Abu Dhabi University)
An Application of Blaschke Products to Algebraic Differential Equations
Thursday, July 28 (Bahen Centre Room 1200) map
Chair: Ulrich Daepp (AM), Joseph Cima (PM)
8:00-8:30 Morning Coffee
8:30-9:30 Dragan Vukotic (Universidad Autónoma de Madrid & ICMAT)
Integrability of the derivatives of Blaschke products and applications
9:30-10:30 Christer Glader (Åbo Akademi University)
Nonlinear Riemann-Hilbert Problems with Circular Target Curves
10:30-10:50 Coffee Break
10:50-11:50 Igor Chyzhykov (Lviv National University)
Growth, zero distribution and factorization of analytic functions of moderate growth in the unit disc
11:50-14:00 Lunch Break
14:00-15:00 Vasiliy Prokhorov (University of South Alabama)
On Approximation of Analytic Functions
15:00-15:30 Patrick Tuen-Wai Ng (University of Hong Kong)
Chebyshev-Blaschke products
15:30-16:00 Gunter Semmler (Fakultät für Mathematik und Informatik)
Interpolation with Blaschke products and phase portraits
16:00-16:20 Coffee Break
16:20-16:50 Andre Boivin (University of Western Ontario)
A Bi-orthogonal Expansion in the Space L2(R+)
16:50-17:20 Stephane Charpentier (Universite Paris Sud)
Composition operators on Hardy-Orlicz and Bergman-Orlicz spaces on the ball
17:20-17:50 Helene Bommier (University of Provence)
Bergman type projections and operators on generalized Fock spaces
Friday, July 29 (Bahen Centre Room 1200) map
Chair: Pamela Gorkin (AM)
8:00-8:30 Morning Coffee
8:30-9:30 Timothy McNicholl (Lamar University)
Blaschke products and inner functions from the viewpoint of the theory of computation
9:30-10:30 Armen Edigarian (Jagiellonian University)
Blaschke products in pluripotential theory
10:30-10:50 Coffee Break
10:50-11:50 Oleg Ivrii (Harvard University)
On the Weil-Petersson metric on the space of Blaschke products
11:50-12:00 Closing Remarks

Conference Speakers


Baratchart, Laurent -- INRIA
Baribeau, Line -- Laval University
Benbourenane, Jamal
--Abu Dhabi University
Chyzhykov, Igor
-- Lviv National University
Cima, Joseph -- University of North Carolina
Daepp, Ulrich -- Bucknell University
Edigarian, Armen-- Jagiellonian University
Fournier, Richard
-- Université de Montréal
Glader, Christer
-- Åbo Akademi University
Gorkin, Pamela -- Bucknell University
Heittokangas, Janne -- University of Joensuu
Kraus, Daniela -- University of Wuerzburg
McNicholl, Timothy -- Lamar University
Nicolau, Artur -- Universitat Autònoma de Barcelona
Pap, Margit
-- University of Vienna
Patrick, Tuen-wai Ng -
-The University of Hong Kong
Prokhorov, Vasiliy
-- University of South Alabama
Rahman, Qazi Ibadur
-- Université de Montréal
Ross, William -- University of Richmond
Roth, Oliver -- University of Würzburg
Semmler, Gunter --
Fakultät für Mathematik und Informatik
Shargorodsky, Eugene -- King's College
Vukotic, Dragan -- Universidad Autónoma de Madrid & ICMAT
Xiao, Jie
-- Memorial University of Newfoundland
Zwonek, Wlodzimierz -- Jagiellonian University

Confirmed Participants as of July 18, 2011

Full Name University Name
Baratchart, Laurent INRIA Sophia Antipolis - Méditerranée
Baribeau, Line Université Laval
Benbourenane, Jamal Abu Dhabi University
Boivin, André University of Western Ontario
Bommier, Hélène Université de Provence
Charpentier, Stéphane Université Paris-Sud
Chyzhykov, Igor Lviv National University
Cima, Joseph University of North Carolina
Daepp, Ulrich Bucknell University
Drissi, Driss Kuwait University
Edigarian, Armen Jagiellonian University
Favorov, Sergii Kharkov National University
Fournier, Richard Université de Montréal
Fricain, Emmanuel Université Claude Bernard Lyon 1
Glader, Christer Åbo Akademi University
Gorkin, Pamela Bucknell University
Heittokangas, Janne University of Joensuu
Ivrii, Oleg Harvard University
Kraus, Daniela University of Wuerzburg
Li, Daniel Université d'Artois
Mashreghi, Javad Université Laval
McNicholl, Timothy Lamar University
Ng, Tuen Wai The University of Hong Kong
Nicolau, Artur Universitat Autonoma de Barcelona
Pap, Margit University of Pécs
Pozzi, Elodie Université Lyon I
Prokhorov, Vasiliy University of South Alabama
Qazi, Mohammed Tuskegee University
Rahman, Qazi Ibadur Université de Montréal
Ross, William University of Richmond
Roth, Oliver University of Würzburg
Schippers, Eric University of Manitoba
Semmler, Gunter Technische Universität Bergakademie Freiberg
Shargorodsky, Eugene King's College London
Vukotic, Dragan Universidad Autónoma de Madrid & ICMAT
Xiao, Jie Memorial University of Newfoundland
Zorboska, Nina University of Manitoba
Zwonek, Wlodzimierz Jagiellonian University
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