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Minimize RSR Award Detail

Research Spending & Results

Award Detail

Awardee:REGENTS OF THE UNIVERSITY OF COLORADO, THE
Doing Business As Name:University of Colorado at Boulder
PD/PI:
  • Robin Deeley
  • (303) 735-7573
  • robin.deeley@colorado.edu
Award Date:03/26/2020
Estimated Total Award Amount: $ 258,217
Funds Obligated to Date: $ 258,217
  • FY 2020=$258,217
Start Date:05/01/2020
End Date:04/30/2023
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:Dynamics, Groupoids, and C*-Algebras
Federal Award ID Number:2000057
DUNS ID:007431505
Parent DUNS ID:007431505
Program:ANALYSIS PROGRAM
Program Officer:
  • Christian Rosendal
  • (703) 292-2571
  • crosenda@nsf.gov

Awardee Location

Street:3100 Marine Street, Room 481
City:Boulder
State:CO
ZIP:80303-1058
County:Boulder
Country:US
Awardee Cong. District:02

Primary Place of Performance

Organization Name:The Regents of the University of Colorado
Street:3100 Marine St, Room 481, 572 UC
City:Boulder
State:CO
ZIP:80303-1058
County:Boulder
Country:US
Cong. District:02

Abstract at Time of Award

One key goal of pure mathematics is to classify highly abstract objects; in doing so, invariants can serve to distinguish different types. The key properties of a useful invariant are that it is computable and that it distinguishes many different objects. It is challenging to determine such invariants for dynamical systems, an important class of mathematical structure. This project studies invariants of dynamical systems using the abstract concepts of operator algebras, in particular C*-algebras. The project will involve significant contributions from early-career researchers, graduate students, and undergraduate students, who will benefit from training through research involvement. In more detail, given a dynamical system one can (often) construct a C*-algebra using a groupoid construction. The K-theory of this C*- algebra is an invariant of the original dynamical system. An important question is to determine the distinguishing power and computability of this invariant at the dynamical system level. The investigator will study the range of the Elliott invariant, which consists of K-theory and tracial information, for C*-algebras constructed from minimal and hyperbolic dynamical systems. The investigator and collaborators will systematically construct minimal dynamical systems with prescribed K-theory and will compute the K-theory of specific examples of C*-algebras associated to hyperbolic dynamical systems called Smale spaces. 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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