Award Abstract # 1743819
CBMS Conference: Smooth and Non-Smooth Harmonic Analysis

NSF Org: DMS
Division Of Mathematical Sciences
Recipient: IOWA STATE UNIVERSITY OF SCIENCE AND TECHNOLOGY
Initial Amendment Date: October 18, 2017
Latest Amendment Date: October 18, 2017
Award Number: 1743819
Award Instrument: Standard Grant
Program Manager: James Matthew Douglass
mdouglas@nsf.gov
 (703)292-2467
DMS
 Division Of Mathematical Sciences
MPS
 Directorate for Mathematical and Physical Sciences
Start Date: February 1, 2018
End Date: January 31, 2019 (Estimated)
Total Intended Award Amount: $35,364.00
Total Awarded Amount to Date: $35,364.00
Funds Obligated to Date: FY 2018 = $35,364.00
History of Investigator:
  • Eric Weber (Principal Investigator)
    esweber@iastate.edu
  • Justin Peters (Co-Principal Investigator)
  • John Herr (Co-Principal Investigator)
Recipient Sponsored Research Office: Iowa State University
1350 BEARDSHEAR HALL
AMES
IA  US  50011-2103
(515)294-5225
Sponsor Congressional District: 04
Primary Place of Performance: Iowa State University
396 Carver Hall
Ames
IA  US  50011-2207
Primary Place of Performance
Congressional District:
Unique Entity Identifier (UEI): DQDBM7FGJPC5
Parent UEI: DQDBM7FGJPC5
NSF Program(s): INFRASTRUCTURE PROGRAM
Primary Program Source: 01001819DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s): 7556
Program Element Code(s): 126000
Award Agency Code: 4900
Fund Agency Code: 4900
Assistance Listing Number(s): 47.049

ABSTRACT

This National Science Foundation award provides support for the Conference Board of the Mathematical Sciences Conference "Harmonic Analysis: Smooth and Non-smooth" to be held at Iowa State University on June 4-8, 2018.  In recent years there has been an increasing interest in understanding the harmonic analysis of non-smooth geometries that are unlike the familiar smooth Euclidean geometry, such as when nearby points are not locally connected to each other.  Real-world examples in which these types of geometry appear include large computer networks, relationships in datasets, and fractal structures such as those found in crystalline substances, light scattering, and other natural phenomena where dynamical systems are present. The proposed conference will consist of a series of ten lectures by Professor Palle Jorgensen from the University of Iowa, a leader in the fields of smooth and non-smooth harmonic analysis, who will in the course of the conference demonstrate the surprising connections between the two domains. The conference aims to bring both experienced and new researchers together to stimulate collaboration on this timely topic.  The broader impacts of the conference include the advancement of underrepresented minorities within mathematics and the development of a globally competitive STEM workforce.  Approximately thirty participants will be supported, many of whom will be current graduate students.  The conference will contribute to those graduate students' educational and professional development and hence prepare the nation's next generation of researchers to engage this increasingly important subject area.

A remarkable and oft-cited result of Professor Jorgensen is that there exists a Cantor-like set with the property that the uniform measure supported on that set is spectral, meaning that there exists a sequence of frequencies for which the corresponding exponential functions form an orthonormal basis in the Hilbert space of square-integrable functions with respect to that measure.  Research that has been inspired by this stunning result includes: fractal Fourier analyses, spectral theory of Ruelle operators, representation theory of Cuntz algebras, convergence of the cascade algorithm in wavelet theory, reproducing kernels and their boundary representations, Bernoulli convolutions, and Markov processes.  The remarkable feature of this array of subjects is that they straddle both the smooth and non-smooth settings.  The lectures presented by Professor Jorgensen will unify these far-reaching research areas at the interface of smooth and non-smooth harmonic analysis, with the corresponding monograph being of great value to current and future researchers as a consolidated reference for these topical connections. Information regarding the conference is at the following URL:  http://www.public.iastate.edu/~esweber/cbms2018/

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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Bond, Bailey Madison and Glickfield, R. Alexander and Herr, John E. "On the existence of complex Hadamard submatrices of the Fourier matrices" Demonstratio Mathematica , v.52 , 2019 10.1515/dema-2019-0001 Citation Details
Harding, Steven N. and Picioroaga, Gabriel "A generalized Walsh system for arbitrary matrices" Demonstratio Mathematica , v.52 , 2019 10.1515/dema-2019-0006 Citation Details
Ionescu, Marius and Savage, Thomas L. "The "hot spots" conjecture on the Vicsek set" Demonstratio Mathematica , v.52 , 2019 10.1515/dema-2019-0003 Citation Details
Yee, Tat-Leung and Ho, Kwok-Pun "Zygmund inequality of the conjugate function on Morrey-Zygmund spaces" Demonstratio Mathematica , v.52 , 2019 10.1515/dema-2019-0011 Citation Details

PROJECT OUTCOMES REPORT

Disclaimer

This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.


The award 1743819, CBMS Conference: Harmonic Analysis: Smooth and Non-Smooth, funded conference participation for a CBMS conference of the same title that took place at Iowa  State University in Ames, IA during the week of June 4-8, 2018.  The centerpiece of the conference was the principal lecture series delivered by Professor Palle Jorgensen,  University of Iowa.  The principal lectures addressed understanding the harmonic analysis of non-smooth geometries that are unlike the familiar smooth Euclidean geometry, such as when nearby points are not locally connected to each other.  Real-world examples in which these types of geometry appear include large computer networks, relationships in datasets, and fractal structures such as those found in crystalline substances, light scattering, and other natural phenomena where dynamical systems are present.  The ten lectures by Professor Jorgensen were augmented by lectures from Kasso Okoudjou, University of Maryland, Marius Ionescu, United States Naval Academy, and Daniel Alpay, Chapman University.

The conference had over 50 participants, including many early career researchers, several undergraduate students, and also established researchers from outside the area of harmonic analysis.  There are several products from the conference: (i) a monograph authored by Professor Jorgensen, (ii) a special issue of a mathematical journal that will publish 6-8 articles by conference participants, including several undergraduate students, and (iii) video recordings of the ten lectures posted at the conference website, which can be found through a web search on the conference title.

A main goal of the conference was to increase the competitiveness of the STEM workforce.  The conference accomplished this goal by bringing together a diversity of mathematicians with a variety of research interests.  In addition, the conference broadened participation among several key groups of national significance.  There were several undergraduate participants who attended the conference, all of whom are either now enrolled or will be enrolling in graduate programs in mathematics.  There were also women and underrepresented minority participants who attended the conference, providing those participants with additional opportunities for conducting research and networking.  Immediate impact of the conference includes increasing the number of PhD students working with Dr. Jorgensen, generating thesis research of those students, and providing opportunities for those students to collaborate with other established researchers across the country.

The conference website is available at: https://faculty.sites.iastate.edu/esweber/cbms-2018

 


Last Modified: 04/02/2019
Modified by: Eric Weber

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