SCIENTIFIC PROGRAMS AND ACTIVITIES

September  2, 2014
WORKSHOP ON THE CORONA PROBLEM:
CONNECTIONS BETWEEN OPERATOR
THEORY, FUNCTION THEORY AND GEOMETRY

June 18-22, 2012
Fields Institute

 


supported in part
by the
National Science
Foundation
DMS1200994

Organizers: Ron Douglas (Texas A&M)
Steven G. Krantz (Washington - St. Louis), Eric T. Sawyer (McMaster)
Sergei Treil (Brown), Brett D. Wick (Georgia Institute of Technology)
Registration on site June 18
Fee $50, Fees waived for students & PDF
audio and slides
Participants Toronto Accommodation in Toronto

Overview

In recent years, there has been a flurry of research activity on the Corona problem. It should be noted that there has never before been a workshop that focuses on the Corona problem in one and several variables and in particular, one that focuses on the interactions between this problem and other areas of analysis. This workshop would bring together researchers from three different areas: harmonic analysis, operator theory, and several complex variables which will lead to further collaborations and interactions among these areas.

Workshop Themes

The Corona Problem, Function Theory and Harmonic Analysis.
Corona in Several Variables.
Corona for Planar Domains.
Completion Problem.

Expository Introductory Talks

A series of talks setting out the major relevant themes in the different subject areas will be a significant aid to the discussion periods the Workshop will have. In the first two days, there will be general surveys on the related themes of the Workshop. These expository talks will be delivered by experts on the subject and will serve to bring the participants unfamiliar with the topics "up to speed".
It is anticipated that these morning talks will be exible and open-ended, with interruptions and questions from the participants.
Additionally, if necessary, there may be another expository talk during the first two days.

Ron Douglas Operator Theory and Complex Geometry
Sergei Treil Corona and Ideal Problems on the Disc
Steven Krantz Several Complex Variables and the Corona Theorem
Eric Sawyer Corona Theorems for Besov-Sobolev Spaces

Subsequent morning talks will be selected and guided based on participant feedback. As the workshop progresses, there will be topics that will become more useful and interesting for the participants and relevant experts from the participants will be selected to provide an expository talk on the subject. The workshop will have an afternoon problem session to discuss potential points of entry into this area of research.

Program : (speakers abstracts)

Monday
9:00-9:25 Onsite Registration and Coffee
9:25-9:30 Workshop Welcome
9:30-10:30 Ron G. Douglas
The Corona Problem and Operator Theory
10:30-11:00 Coffee Break
11:00-12:00 Steven G. Krantz
The Corona Problem In Several Complex Variables
12:00-2:00 Lunch
2:00-3:00 Eric T. Sawyer
Corona theorems for the Drury-Arveson space and other Besov-Sobolev spaces of
holomorphic functions on the ball
3:00-3:30 Tea Break
3:30-4:00 Mishko Mitkovski
Compactness of operators on Bergman type spaces
4:00-5:30 Reception at Fields
Tuesday
9:00-9:30 Morning Coffee
9:30-10:30 Sergei Treil
Corona, ideals, and the completion problem: a geometric approach
10:30-11:00 Coffee Break
11:00-12:00 Tavan Trent
Remarks on Corona Problems
12:00-2:00 Lunch
2:00-3:00 Alexander Brudnyi
Stein-like Theory for Banach-valued Holomorphic Functions on the Maximal Ideal
space of H ∞ and the Operator Corona Problem of Sz.-Nagy
3:00-3:30 Tea Break
3:30-4:00 Kelly Bickel
Inner Functions and associated Hilbert Spaces on the Bidisk
4pm- Open
Wednesday
9:00-2:00 Free
2:00-3:00 Open Problem Session
3:00-3:30 Tea Break
3:30-4:30 Back2Fields Colloquium: Brett D. Wick
Thursday
9:00-9:30 Morning Coffee
9:30-10:30 Nikolai Nikolskii
Numerically Effective Corona Problems
10:30-11:00 Coffee Break
11:00-12:00 Amol Sasane
The corona and completion problem for an algebra of measures used in control theory
12:00-2:00 Lunch
2:00-3:00 Greg Knese
Inner functions on the bidisk and associated Hilbert spaces
3:00-3:30 Tea Break
3:30-4:00 Ryan Hamilton
The Toeplitz Corona Problem and a Distance Formula
4pm- Open
Friday
9:00-9:30 Morning Coffee
9:30-10:30 Ken Davidson
Classification of Universal Operator Algebras associated to Varieties
10:30-11:00 Coffee Break
11:00-12:00 Richard Rochberg
Truncated Hankel forms, Hankel forms on Model Spaces
12:00-12:30 Debendra Banjade
Wolff 's Corona Problem in the Multiplier Algebra of the Dirichlet Space in the unit
disk

Final Participant List


Full Name University/Affiliation
Agler, James University of California, San Diego
Banjade, Debendra University of Alabama
Benge, Philip Georgia Institute of Technology
Bernucci, Daniel Georgia Institute of Technology
Bickel, Kelly Washington University in St. Louis
Brudnyi, Alexander University of Calgary
Castillo, Miriam University of Florida
Chen, Liwei Washington University in St. Louis
Condori, Alberto Florida Gulf Coast University
Davidson, Kenneth University of Waterloo
Di Biase, Fausto Universita' "G. D'Annunzio"
Douglas, Ronald G. Texas A&M University
Ferguson, Tim Vanderbilt University
Gorai, Sushil Indian Statistical Institute
Hamilton, Ryan University of Waterloo
Jury, Michael University of Florida
Kennedy, Matthew Carleton University
Kinzebulatov, Damir The Fields Institute
Knese, Gregory University of Alabama
Krantz, Steven Washington University in St. Louis
Lee, Lina University of California, Riverside
Li, Song-Ying University of California, Irvine
Li, Zhiqiang Fields Institute
Liu, Bingyuan Washington University in St. Louis
Mitkovski, Mishko Georgia Institute of Technology
Nikolski, Nikolai K. Université Bordeaux 1
Oh, Byung-Geun Hanyang University
Pal, Sourav Indian Statistical Institute
Patel, Sanjay McMaster University
Pau, Jordi Universitat de Barcelona
Petzka, Henning University of Toronto
Rochberg, Richard Washington University
Sarfatti, Giulia University of Florence
Sasane, Amol London School of Economics
Sawyer, Eric McMaster University
Sunkes, James University of Tennessee-Knoxville
Treil, Sergei Brown University
Trent, Tavan University of Alabama
Wick, Brett Georgia Institute of Technology
Xiao, Jie Memorial University of Newfoundland
Xu, Wen Memorial University of Newfoundland
Yang, Dilian University of Windsor
Zeytuncu, Yunus Texas A&M University
Zhou, Cong McMaster University
Zhu, Kehe State University of New York at Albany
Zorboska, Nina University of Manitoba