Organizing Committee
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.

Image for "Frame Theory and Exponential Bases "

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, June 4, 2018
TimeEventLocationMaterials
9:00 - 9:25am EDTRegistration - ICERM 121 South Main Street, Providence RI 0290311th Floor Collaborative Space 
9:25 - 9:30am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:30 - 10:20am EDTExponential frames and syndetic Riesz sequences - Marcin Bownik, University of Oregon11th Floor Lecture Hall
10:20 - 10:50am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:50 - 11:40am EDTToeplitz Methods In Gap And Spectral Problems - Alexei Poltoratski, Texas A&M University11th Floor Lecture Hall
11:50 - 12:40pm EDTThe Wavelet Existence Problem - Darrin Speegle, Saint Louis University11th Floor Lecture Hall
12:40 - 2:20pm EDTBreak for Lunch / Free Time  
2:20 - 3:10pm EDTFuglede's tiling-spectrality conjecture for convex polytopes - Nir Lev, Bar-Ilan University11th Floor Lecture Hall
3:10 - 3:40pm EDTCoffee/Tea Break 11th Floor Collaborative Space 
3:40 - 4:30pm EDTSpectrality of Product Domains - Rachel Greenfeld, Bar Ilan University11th Floor Lecture Hall
4:40 - 6:10pm EDTWelcome Reception/ Poster Session11th Floor Collaborative Space 
Tuesday, June 5, 2018
TimeEventLocationMaterials
9:30 - 10:20am EDTFuglede's spectral set conjecture on cyclic groups - Romanos Malikiosis, TU Berlin11th Floor Lecture Hall
10:20 - 10:50am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:50 - 11:40am EDTDiscrete Translates in Function Spaces. - Alexander Olevskii, Tel Aviv University, School of Math.11th Floor Lecture Hall
11:50 - 12:40pm EDTBalian-Low type theorems for finite sequences - Jan-Fredrik Olsen, Lund University11th Floor Lecture Hall
12:40 - 2:20pm EDTBreak for Lunch / Free Time  
2:20 - 3:10pm EDTFrames generated from exponential of operators. - Akram Aldroubi, Vanderbilt University11th Floor Lecture Hall
3:10 - 3:40pm EDTCoffee/Tea Break 11th Floor Collaborative Space 
3:40 - 4:30pm EDTOn Convergence of Rearranged Fourier Series - Keaton Hamm, Vanderbilt University11th Floor Lecture Hall
4:40 - 5:10pm EDTOpen problems in spectral theory - Alexei Poltoratski, Texas A&M University11th Floor Lecture Hall 
Wednesday, June 6, 2018
TimeEventLocationMaterials
9:30 - 10:20am EDTA survey of applications of geometric combinatorics in frame theory  - Alex Iosevich, University of Rochester11th Floor Lecture Hall
10:20 - 10:50am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:50 - 11:40am EDTInterpolating sequences by polynomials - Joaquim Ortega-Cerdà, University of Barcelona11th Floor Lecture Hall
11:50 - 12:40pm EDTPositive definite functions and the problem of mutually unbiased bases - Mate Matolcsi, Budapest University of Technology11th Floor Lecture Hall
12:40 - 2:20pm EDTBreak for Lunch / Free Time  
2:20 - 3:10pm EDTThe Fuglede conjecture holds in Zp × Zp - Azita Mayeli, City University of New York11th Floor Lecture Hall
3:10 - 3:40pm EDTCoffee/Tea Break 11th Floor Collaborative Space 
3:40 - 4:30pm EDTUncertainty Principles for Fourier Multipliers - Michael Northington, Georgia Institute of Technology11th Floor Lecture Hall
4:40 - 5:10pm EDTOpen problems regarding mutually unbiased bases - Mate Matolcsi, Budapest University of Technology11th Floor Lecture Hall
Thursday, June 7, 2018
TimeEventLocationMaterials
9:30 - 10:20am EDTThree bases and other tricks to replace Hankel and Toeplitz - Stefanie Petermichl, Université Paul Sabatier11th Floor Lecture Hall
10:20 - 10:50am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:50 - 11:40am EDTThe Newman-Shapiro problem - Alexander Borichev, Aix-Marseille University11th Floor Lecture Hall
11:50 - 12:40pm EDTRiesz 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 EDTBreak for Lunch / Free Time  
2:20 - 3:10pm EDTFew remarks on the uncertainty principle. - Mishko Mitkovski, Clemson University11th Floor Lecture Hall
3:10 - 3:40pm EDTCoffee/Tea Break 11th Floor Collaborative Space 
3:40 - 4:30pm EDTSome open problems related to exponential systems - Shahaf Nitzan, Georgia Tech11th Floor Lecture Hall
4:40 - 5:10pm EDTOpen problems in wavelet theory - Marcin Bownik, University of Oregon11th Floor Lecture Hall
Friday, June 8, 2018
TimeEventLocationMaterials
9:30 - 10:20am EDTHausdorff operators in $H^p$ spaces, $0 - Elijah Liflyand, Bar-Ilan University11th Floor Lecture Hall
10:20 - 10:50am EDTCoffee/Tea Break 11th Floor Collaborative Space 
10:50 - 11:40am EDTSome open problems about tilings and spectra - Mihalis Kolountzakis, University of Crete11th Floor Lecture Hall
11:50 - 12:40pm EDTNonnegativity for structured complete systems - Alex Powell, Vanderbilt University11th Floor Lecture Hall
12:40 - 2:20pm EDTBreak for Lunch / Free Time  
2:20 - 3:10pm EDTFourier frame for singular measures - Chun-Kit Lai, San Francisco State University11th Floor Lecture Hall
3:10 - 3:40pm EDTCoffee/Tea Break 11th Floor Collaborative Space 
3:40 - 4:30pm EDTMulti-tiling and equidecomposability of polytopes by lattice translates - Bochen Liu, Bar-Ilan University11th Floor Lecture Hall

Lecture Videos

Multi-tiling and equidecomposability of polytopes by lattice translates

Bochen Liu
Bar-Ilan University
June 8, 2018
Frame Theory and Exponential Bases
Play     Abstract     Slides

Fourier frame for singular measures

Chun Kit Lai
San Francisco State University
June 8, 2018
Frame Theory and Exponential Bases
Play     Abstract

Some open problems about tilings and spectra

Mihalis Kolountzakis
University of Crete
June 8, 2018
Frame Theory and Exponential Bases
Play     Abstract

Hausdorff operators in $H^p$ spaces, $0

Elijah Liflyand
Bar-Ilan University
June 8, 2018
Frame Theory and Exponential Bases
Play     Abstract     Slides

Few remarks on the uncertainty principle

Mishko Mitkovski
Clemson University
June 7, 2018
Frame Theory and Exponential Bases
Play     Abstract

Riesz bases, Meyer's quasicrystals and bounded remainder sets

Sigrid Grepstad
Norwegian University of Science and Technology
June 7, 2018
Frame Theory and Exponential Bases
Play     Abstract     Slides

The Newman-Shapiro problem

Alexander Borichev
Univ. Aix-Marseille
June 7, 2018
Frame Theory and Exponential Bases
Play     Abstract

Three bases and other tricks to replace Hankel and Toeplitz

Stefanie Petermichl
Université Paul Sabatier
June 7, 2018
Frame Theory and Exponential Bases
Play     Abstract

Uncertainty Principles for Fourier Multipliers

Michael Northington
Georgia Institute of Technology
June 6, 2018
Frame Theory and Exponential Bases
Play     Abstract     Slides

The Fuglede Conjecture holds in Zp x Zp

Azita Mayeli
CUNY
June 6, 2018
Frame Theory and Exponential Bases
Play     Abstract

Positive definite functions and the problem of mutually unbiased bases

Máté Matolcsi
Renyi Institute
June 6, 2018
Frame Theory and Exponential Bases
Play     Abstract     Slides

Interpolating real polynomials

Joaquim Ortega-Cerdà
University of Barcelona
June 6, 2018
Frame Theory and Exponential Bases
Play     Abstract     Slides

A survey of applications of geometric combinatorics in frame theory

Alex Iosevich
University of Rochester
June 6, 2018
Frame Theory and Exponential Bases
Play     Abstract

On Convergence of Rearranged Fourier Series

Keaton Hamm
Vanderbilt University
June 5, 2018
Frame Theory and Exponential Bases
Play     Abstract

Frames generated from exponential of operators

Akram Aldroubi
Vanderbilt University
June 5, 2018
Frame Theory and Exponential Bases
Play     Abstract     Slides

Balian-Low type theorems for finite sequences

Jan-Fredrik Olsen
Lund University
June 5, 2018
Frame Theory and Exponential Bases
Play     Abstract

Discrete Translates in Function Spaces

Alexander Olevskii
Tel Aviv University
June 5, 2018
Frame Theory and Exponential Bases
Play     Abstract

Fuglede's spectral set conjecture on cyclic groups

Romanos Malikiosis
TU Berlin
June 5, 2018
Frame Theory and Exponential Bases
Play     Abstract     Slides

Spectrality of Product Domains

Rachel Greenfeld
Bar Ilan University
June 4, 2018
Frame Theory and Exponential Bases
Play     Abstract

Fuglede's tiling-spectrality conjecture for convex polytopes

Nir Lev
Bar-Ilan University
June 4, 2018
Frame Theory and Exponential Bases
Play     Abstract

The Wavelet Existence Problem

Darrin Speegle
Saint Louis University
June 4, 2018
Frame Theory and Exponential Bases
Play     Abstract

Toeplitz Methods In Gap And Spectral Problems

Alexei Poltoratski
Texas A&M University
June 4, 2018
Frame Theory and Exponential Bases
Play     Abstract

Exponential frames and syndetic Riesz sequences

Marcin Bownik
University of Oregon
June 4, 2018
Frame Theory and Exponential Bases
Play     Abstract     Slides