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Faraway Fourier Talks

The Norbert Wiener Center Online Seminar on Harmonic Analysis and Applications

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When:
Mondays at 11 a.m. PST / 2 p.m. EST / 8 p.m. CET

Where:
Zoom. For access to the Zoom link, please join the mailing list by entering your information here.

Recorded talks are on our Youtube channel.

Upcoming Talks:

 November 2nd, 2020  Ursula Molter (University of Buenos Aires)  Riesz Bases of Exponentials and the Bohr Topology
In this talk we address the question of what domains Ω of Rd with finite measure, admit a Riesz basis of exponentials, that is, the existence of a discrete set B ⊂ Rd such that the exponentials E(B) = {e2piß·ω : ß ∈ B} form a Riesz basis of L2(Ω). Using the Bohr compactification of the integers, we show a necessary and sufficient condition to ensure that a multi-tile Ω subset of Rd of positive measure (but not necessarily bounded) admits a structured Riesz basis of exponentials for L2(Ω). Here a set Ω ⊂ Rd is a k-multi-tile for Zd if Σλ ∈ Zd ΧΩ(ω - λ) = k a.e. ω ∈ Rd.
 November 9th, 2020  Jill Pipher (Brown University)
 November 16th, 2020  Jean Pierre Gabardo (McMaster University)
 November 23rd, 2020, 2:30pm EST  Tomaso Poggio (MIT)
 November 30th, 2020  Carlos Cabrelli (University of Buenos Aires)
 December 7th, 2020  Palle Jorgensen (University of Iowa)
 December 14th, 2020  Gil Strang (MIT)
 December 21st, 2020  Vivek Goyal (Boston University)
 January 4th, 2021  Qiyu Sun (University of Central Florida)
 January 11th, 2021  Victor Wickerhauser (Washington University in St. Louis)
 January 25th, 2021  Andrea Bertozzi (UCLA)
 Febuary 1st, 2021  Michael Lacey (Georgia Tech)
 Febuary 8th, 2021  Alfred Hero (University of Michigan)
 Febuary 15th, 2021  Akram Aldroubi (Vanderbilt University)
 Febuary 22nd, 2021  Pete Casazza (University of Missouri)
 March 1st, 2021  Marcin Bownik (University of Oregon)
 March 8th, 2021  Rodolfo Torres (University of California, Riverside)

Previous Talks:

 October 26th, 2020  Virginia Naibo (Kansas State University)  Fractional Leibniz Rules: A Guided Tour
The usual Leibniz rules express the derivative of a product of functions in terms of the derivatives of each of the factors. In an analogous sense, fractional Leibniz rules involve the concept of fractional derivative and provide estimates of the size and smoothness of a product of functions in terms of the size and smoothness of each of the factors. These bilinear estimates stem from the study of partial differential equations such as Euler, Navier Stokes and Korteweg-de Vries. In this talk, I will present fractional Leibniz rules associated to bilinear pseudodifferential operators with homogeneous symbols, including Coifman-Meyer multipliers, and with symbols in the bilinear Hörmander classes. Through different approaches, the estimates will be discussed in the settings of weighted Lebesgue, Triebel-Lizorkin and Besov spaces.
 October 19th, 2020  Ronald Coifman (Yale)  Phase Unwinding Analysis: Nonlinear Fourier Transforms and Complex Dynmaics
Our goal here is to introduce recent developments of analysis of highly oscillatory functions. In particular we will sketch methods extending conventional Fourier analysis, exploiting both phase and amplitudes of holomorphic functions. The miracles of nonlinear complex holomorphic analysis, such as factorization and composition of functions lead to new versions of holomorphic orthonormal bases , relating them to multiscale dynamical systems, obtained by composing Blaschke factors. We also, remark, that the phase of a Blaschke product is a one-layer neural net with (arctan as an activation sigmoid) and that the composition is a "Deep Neural Net" whose depth is the number of compositions, our results provide a wealth of related libraries of orthogonal bases . We will also indicate a number of applications in medical signal processing , as well in precision Doppler. Each droplet in the phase image below represent a unit of a two layers deep net and gives rise to an orthonormal basis the Hardy space
 October 12th, 2020  Alex Iosevich (University of Rochester)  Finite Point Configurations and Applications to Frame Theory
We are going to discuss some recent developments in the study of finite point configuration in sets of a given Hausdorff dimension. We shall also survey some applications of the finite point configuration machinery to the problems of existence and non-existence of exponential/Gabor bases and frames.

Organizing Committee:
Wojtek Czaja
Radu Balan
Jacob Bedrossian
John Benedetto
Vince Lyzinski
Thomas Goldstein
Ray Schram



 

In cooperation with

SIAM

 

Now in Print!
Excursions in Harmonic Analysis:
The Fall Fourier Talks at the Norbert Wiener Center

Excursions in Harmonic Analysis, Volume 1 Excursions in Harmonic Analysis, Volume 2
Excursions in Harmonic Analysis, Volume 3 Excursions in Harmonic Analysis, Volume 4
Excursions in Harmonic Analysis, Volume 5

 

 




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Norbert Wiener Center
Department of Mathematics
University of Maryland
College Park, MD 20742
Phone: (301) 405-5158
The Norbert Wiener Center is part of the College of Computer, Mathematical, and Natural Sciences.