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Research Spending & Results

Award Detail

Awardee:BROWN UNIVERSITY IN PROVIDENCE IN THE STATE OF RHODE ISLAND AND PROVIDENCE PLANTATIONS
Doing Business As Name:Brown University
PD/PI:
  • Georgios D Daskalopoulos
  • (401) 863-1136
  • daskal@math.brown.edu
Award Date:08/03/2021
Estimated Total Award Amount: $ 454,629
Funds Obligated to Date: $ 454,629
  • FY 2021=$454,629
Start Date:08/15/2021
End Date:07/31/2024
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:Variational Methods in Singular Geometry
Federal Award ID Number:2105226
DUNS ID:001785542
Parent DUNS ID:001785542
Program:GEOMETRIC ANALYSIS
Program Officer:
  • Krishnan Shankar
  • (703) 292-4703
  • kshankar@nsf.gov

Awardee Location

Street:BOX 1929
City:Providence
State:RI
ZIP:02912-9002
County:Providence
Country:US
Awardee Cong. District:01

Primary Place of Performance

Organization Name:Brown University
Street:151 Thayer Street
City:Providence
State:RI
ZIP:02912-9002
County:Providence
Country:US
Cong. District:01

Abstract at Time of Award

Physical phenomena tend to obey the least action principle, namely moving in trajectories that make the action locally stationary. If the action is given by Dirichlet energy, then the stationary points are in some cases geodesics (shortest paths), and in other cases harmonic functions and various generalizations of these notions familiar from elementary physics. In this project, the PI will study stationary solutions either related to harmonic maps obtained by minimizing Dirichlet energy or best Lipschitz maps (sometimes called infinity harmonic) obtained by minimizing Lipschitz constants. Both problems have interesting applications to geometric topology and group theory. The project also includes significant training and mentoring of junior mathematicians (students, post-doctoral researchers, junior faculty) The work of Eells-Sampson in the 60's launched an explosion of research for harmonic maps between Riemannian manifolds. Many important applications followed in minimal surface theory, Kaehler geometry and rigidity of group actions on manifolds among others. More recently, the seminal work of Gromov-Schoen and Korevaar-Schoen on harmonic maps to metric space targets initiated major progress in understanding phenomena associated with singular spaces, like rigidity of groups acting on buildings and the completion of Teichmueller space. In the first part of the project PI will study several problems in harmonic map theory for singular geometry with applications to Teichmueller theory. In the second part PI will study the calculus of variations of functionals associated with the sup-norm of the gradient of maps between Riemannian manifolds. Such functionals yield solutions of fully non-linear degenerate PDE's with very challenging regularity properties and whose singular set gives geometric realizations of topological objects like geodesic foliations and laminations related to Thurston theory. The PI will also train graduate students and maintains a robust mentoring program for all junior researchers in his department. The latter provides guidance and support to post-doctoral researchers and junior faculty on a range of issues related to professional development. 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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