Frame Theory and Exponential Bases Jun 4 - 8, 2018 Navigate Page
Abstract The problem of decomposing a function into a sum of simply structured functions is a classical area of research in Analysis. Exciting recent progress, e.g. the solution to the Kadison-Singer problem, results about exponential frames and Riesz bases in various settings, and results about orthogonal exponential bases for convex polytopes, has re-energized discussion in this area, opened new directions for study, and turned it into an even more active and fruitful area for research. The goal of this workshop is to discuss such new developments in this area. In particular, the workshop will focus on problems regarding exponential systems in weighted spaces and the Fuglede conjecture. Related settings will also be of interest, for example: (i) Systems of vectors obtained by translating, translating and modulating, or translating and dilating a single function over the line; (ii) Sampling and decomposition of functions in the finite dimensional setting; (iii) Sampling and interpolation of functions in analytic function spaces.
Confirmed Speakers & Participants
Talks will be presented virtually or in-person as indicated in the schedule below.
Workshop Schedule Time Event Location Materials 9:00 - 9:25am EDT Registration - ICERM 121 South Main Street, Providence RI 02903 11th Floor Collaborative Space 9:25 - 9:30am EDT Welcome - ICERM Director 11th Floor Lecture Hall 9:30 - 10:20am EDT Exponential frames and syndetic Riesz sequences - Marcin Bownik, University of Oregon 11th Floor Lecture Hall 10:20 - 10:50am EDT Coffee/Tea Break 11th Floor Collaborative Space 10:50 - 11:40am EDT Toeplitz Methods In Gap And Spectral Problems - Alexei Poltoratski, Texas A&M University 11th Floor Lecture Hall 11:50 - 12:40pm EDT The Wavelet Existence Problem - Darrin Speegle, Saint Louis University 11th Floor Lecture Hall 12:40 - 2:20pm EDT Break for Lunch / Free Time 2:20 - 3:10pm EDT Fuglede's tiling-spectrality conjecture for convex polytopes - Nir Lev, Bar-Ilan University 11th Floor Lecture Hall 3:10 - 3:40pm EDT Coffee/Tea Break 11th Floor Collaborative Space 3:40 - 4:30pm EDT Spectrality of Product Domains - Rachel Greenfeld, Bar Ilan University 11th Floor Lecture Hall 4:40 - 6:10pm EDT Welcome Reception/ Poster Session 11th Floor Collaborative Space
Time Event Location Materials 9:30 - 10:20am EDT Fuglede's spectral set conjecture on cyclic groups - Romanos Malikiosis, TU Berlin 11th Floor Lecture Hall 10:20 - 10:50am EDT Coffee/Tea Break 11th Floor Collaborative Space 10:50 - 11:40am EDT Discrete Translates in Function Spaces. - Alexander Olevskii, Tel Aviv University, School of Math. 11th Floor Lecture Hall 11:50 - 12:40pm EDT Balian-Low type theorems for finite sequences - Jan-Fredrik Olsen, Lund University 11th Floor Lecture Hall 12:40 - 2:20pm EDT Break for Lunch / Free Time 2:20 - 3:10pm EDT Frames generated from exponential of operators. - Akram Aldroubi, Vanderbilt University 11th Floor Lecture Hall 3:10 - 3:40pm EDT Coffee/Tea Break 11th Floor Collaborative Space 3:40 - 4:30pm EDT On Convergence of Rearranged Fourier Series - Keaton Hamm, Vanderbilt University 11th Floor Lecture Hall 4:40 - 5:10pm EDT Open problems in spectral theory - Alexei Poltoratski, Texas A&M University 11th Floor Lecture Hall
Time Event Location Materials 9:30 - 10:20am EDT A survey of applications of geometric combinatorics in frame theory - Alex Iosevich, University of Rochester 11th Floor Lecture Hall 10:20 - 10:50am EDT Coffee/Tea Break 11th Floor Collaborative Space 10:50 - 11:40am EDT Interpolating sequences by polynomials - Joaquim Ortega-Cerdà, University of Barcelona 11th Floor Lecture Hall 11:50 - 12:40pm EDT Positive definite functions and the problem of mutually unbiased bases - Mate Matolcsi, Budapest University of Technology 11th Floor Lecture Hall 12:40 - 2:20pm EDT Break for Lunch / Free Time 2:20 - 3:10pm EDT The Fuglede conjecture holds in Zp × Zp - Azita Mayeli, City University of New York 11th Floor Lecture Hall 3:10 - 3:40pm EDT Coffee/Tea Break 11th Floor Collaborative Space 3:40 - 4:30pm EDT Uncertainty Principles for Fourier Multipliers - Michael Northington, Georgia Institute of Technology 11th Floor Lecture Hall 4:40 - 5:10pm EDT Open problems regarding mutually unbiased bases - Mate Matolcsi, Budapest University of Technology 11th Floor Lecture Hall
Time Event Location Materials 9:30 - 10:20am EDT Three bases and other tricks to replace Hankel and Toeplitz - Stefanie Petermichl, Université Paul Sabatier 11th Floor Lecture Hall 10:20 - 10:50am EDT Coffee/Tea Break 11th Floor Collaborative Space 10:50 - 11:40am EDT The Newman-Shapiro problem - Alexander Borichev, Aix-Marseille University 11th Floor Lecture Hall 11:50 - 12:40pm EDT Riesz bases, Meyer's quasicrystals and bounded remainder sets - Sigrid Grepstad, Norwegian University of Science and Technology (NTNU) 11th Floor Lecture Hall 12:40 - 2:20pm EDT Break for Lunch / Free Time 2:20 - 3:10pm EDT Few remarks on the uncertainty principle. - Mishko Mitkovski, Clemson University 11th Floor Lecture Hall 3:10 - 3:40pm EDT Coffee/Tea Break 11th Floor Collaborative Space 3:40 - 4:30pm EDT Some open problems related to exponential systems - Shahaf Nitzan, Georgia Tech 11th Floor Lecture Hall 4:40 - 5:10pm EDT Open problems in wavelet theory - Marcin Bownik, University of Oregon 11th Floor Lecture Hall
Time Event Location Materials 9:30 - 10:20am EDT Hausdorff operators in $H^p$ spaces, $0 - Elijah Liflyand, Bar-Ilan University 11th Floor Lecture Hall 10:20 - 10:50am EDT Coffee/Tea Break 11th Floor Collaborative Space 10:50 - 11:40am EDT Some open problems about tilings and spectra - Mihalis Kolountzakis, University of Crete 11th Floor Lecture Hall 11:50 - 12:40pm EDT Nonnegativity for structured complete systems - Alex Powell, Vanderbilt University 11th Floor Lecture Hall 12:40 - 2:20pm EDT Break for Lunch / Free Time 2:20 - 3:10pm EDT Fourier frame for singular measures - Chun-Kit Lai, San Francisco State University 11th Floor Lecture Hall 3:10 - 3:40pm EDT Coffee/Tea Break 11th Floor Collaborative Space 3:40 - 4:30pm EDT Multi-tiling and equidecomposability of polytopes by lattice translates - Bochen Liu, Bar-Ilan University 11th Floor Lecture Hall
Lecture Videos Bochen Liu
Bar-Ilan University
June 8, 2018
Chun Kit Lai
San Francisco State University
June 8, 2018
Mihalis Kolountzakis
University of Crete
June 8, 2018
Elijah Liflyand
Bar-Ilan University
June 8, 2018
Mishko Mitkovski
Clemson University
June 7, 2018
Sigrid Grepstad
Norwegian University of Science and Technology
June 7, 2018
Alexander Borichev
Univ. Aix-Marseille
June 7, 2018
Stefanie Petermichl
Université Paul Sabatier
June 7, 2018
Michael Northington
Georgia Institute of Technology
June 6, 2018
Máté Matolcsi
Renyi Institute
June 6, 2018
Joaquim Ortega-Cerdà
University of Barcelona
June 6, 2018
Alex Iosevich
University of Rochester
June 6, 2018
Keaton Hamm
Vanderbilt University
June 5, 2018
Akram Aldroubi
Vanderbilt University
June 5, 2018
Jan-Fredrik Olsen
Lund University
June 5, 2018
Alexander Olevskii
Tel Aviv University
June 5, 2018
Romanos Malikiosis
TU Berlin
June 5, 2018
Rachel Greenfeld
Bar Ilan University
June 4, 2018
Nir Lev
Bar-Ilan University
June 4, 2018
Darrin Speegle
Saint Louis University
June 4, 2018
Alexei Poltoratski
Texas A&M University
June 4, 2018
Marcin Bownik
University of Oregon
June 4, 2018
