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Research Spending & Results

Award Detail

Awardee:UNIVERSITY OF NEW MEXICO, THE
Doing Business As Name:University of New Mexico
PD/PI:
  • Terry A Loring
  • (505) 277-4613
  • loring@math.unm.edu
Award Date:05/27/2021
Estimated Total Award Amount: $ 119,972
Funds Obligated to Date: $ 119,972
  • FY 2021=$119,972
Start Date:07/01/2021
End Date:06/30/2024
Transaction Type:Grant
Agency:NSF
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.049
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:Numerical Methods in Noncommutative Matrix Analysis
Federal Award ID Number:2110398
DUNS ID:868853094
Parent DUNS ID:784121725
Program:COMPUTATIONAL MATHEMATICS
Program Officer:
  • Malgorzata Peszynska
  • (703) 292-2811
  • mpeszyns@nsf.gov

Awardee Location

Street:1700 Lomas Blvd. NE, Suite 2200
City:Albuquerque
State:NM
ZIP:87131-0001
County:Albuquerque
Country:US
Awardee Cong. District:01

Primary Place of Performance

Organization Name:University of New Mexico
Street:Dept. Mathematics & Statistics
City:Albuquerque
State:NM
ZIP:87131-0001
County:Albuquerque
Country:US
Cong. District:01

Abstract at Time of Award

The project will develop algorithms that are useful for modern physics and quantum information. In particular, the methods developed will be important for modeling topological lasers which are applicable to photonic chips and quantum circuitry. These applications pose challenges to the computational science and in particular to the linear algebra algorithms so they can work with joint measurement in multivariable setting and incommensurate observables recognizing the theoretical limits that exist. The project will consider a variety of multivariable linear algebra algorithms, mainly those filling an immediate need in computational quantum physics and quantum information, but also those that can increase the speed and accuracy of computer shape analysis. The project will involve students and provide training in interdisciplinary projects. This project will develop numerical methods for collections of matrices and operators arising in quantum physics and image analysis. This includes algorithms that work with finite-dimensional approximations to infinite-dimensional systems, leading to better computer modeling of quasicrystals, amorphous systems and periodic systems with defects. Methods and algorithms to be developed will be useful in the study of topological insulators, including periodically-driven systems. The project will study various forms of spectra, including variations of the local density of states, a standard tool in many areas of physics and chemistry. The anticipated work on K-theory is expected to produce new and better tools that can be used by theoretical physicists in numerical studies. At the core of these methods is the study of joint approximate eigenvectors. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

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