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Minimize RSR Award Detail

Research Spending & Results

Award Detail

Awardee:UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL
Doing Business As Name:University of North Carolina at Chapel Hill
PD/PI:
  • Cris Negron
  • (617) 253-4381
  • cnegron@email.unc.edu
Award Date:07/11/2020
Estimated Total Award Amount: $ 156,000
Funds Obligated to Date: $ 156,000
  • FY 2020=$156,000
Start Date:07/15/2020
End Date:06/30/2023
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:Quantum Groups, Support Theory, and Conformal Field Theories
Federal Award ID Number:2001608
DUNS ID:608195277
Parent DUNS ID:142363428
Program:ALGEBRA,NUMBER THEORY,AND COM
Program Officer:
  • James Matthew Douglass
  • (703) 292-2467
  • mdouglas@nsf.gov

Awardee Location

Street:104 AIRPORT DR STE 2200
City:CHAPEL HILL
State:NC
ZIP:27599-1350
County:Chapel Hill
Country:US
Awardee Cong. District:04

Primary Place of Performance

Organization Name:University of North Carolina Department of Mathematics
Street:
City:Chapel Hill
State:NC
ZIP:27599-3250
County:Chapel Hill
Country:US
Cong. District:04

Abstract at Time of Award

This project will establish a new framework that connects the physics of certain two-dimensional physical systems, called conformal field theories (CFTs), with the mathematics of certain well-studied algebraic objects, called quantum groups. Establishing such a connection will greatly advance our understanding of both subjects, and provide novel tools for studying two-dimensional CFTs. In implementing this project, new research opportunities will be created for undergraduates and early graduate students. These research opportunities will be supported by grant funding. The PI will also provide direct support for preexisting programs which seek to increase access to mathematics among women and underrepresented minorities. In more detail, one component of the project is to find an equivalence of (ribbon tensor) categories between the representation category of the so-called triplet vertex algebra, and the representation category of small quantum SL(2). Such an equivalence was conjectured by mathematical physicists in the mid-2000’s, and some explicit progress has been made towards its resolution in recent works of the PI and others. A positive resolution to this conjecture will provide the first direct link between logarithmic CFTs and quantum groups, a phenomenon which should be endemic among the most fundamental classes of logarithmic CFTs. A second component of the project is the computation of the Balmer spectrum for small quantum groups associated to arbitrary simple algebraic groups. This computation will employ and establish new links between support theory and geometric representation theory. 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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