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Research Spending & Results

Award Detail

Awardee:CARNEGIE MELLON UNIVERSITY
Doing Business As Name:Carnegie-Mellon University
PD/PI:
  • Florian Frick
  • (412) 268-5608
  • frick@cmu.edu
Award Date:06/16/2021
Estimated Total Award Amount: $ 400,000
Funds Obligated to Date: $ 60,494
  • FY 2021=$60,494
Start Date:09/01/2021
End Date:08/31/2026
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:CAREER: Geometric and Topological Combinatorics
Federal Award ID Number:2042428
DUNS ID:052184116
Parent DUNS ID:052184116
Program:Combinatorics
Program Officer:
  • Stefaan De Winter
  • (703) 292-2599
  • sgdewint@nsf.gov

Awardee Location

Street:5000 Forbes Avenue
City:PITTSBURGH
State:PA
ZIP:15213-3815
County:Pittsburgh
Country:US
Awardee Cong. District:18

Primary Place of Performance

Organization Name:Carnegie-Mellon University
Street:5000 Forbes Avenue
City:PITTSBURGH
State:PA
ZIP:15213-3815
County:Pittsburgh
Country:US
Cong. District:18

Abstract at Time of Award

Geometry and topology are mathematical branches that provide methods that measure phenomena that are global instead of local. If a problem's resolution depends on the aggregate of its information then geometric methods are useful in detecting global obstructions. Numerous problems across mathematics and its applications are global in this sense, ranging from data science to economics. The research supported by this grant will develop new topological and geometric methods to tackle problems further afield, primarily discrete, non-continuous problems. This promises new insights at the confluence of combinatorics, geometry, and topology. Students at all stages will be involved in the research effort supported by this grant. Among the general goals of the research program are the following: In applications of equivariant topology one often requires that a certain parameter has to be a prime power, and methods fail outside of this prime power case. Recent research of the PI has suggested that one may effectively circumvent this prime power requirement via a synthesis of topological and combinatorial techniques. This will be further developed. The application of topological methods brings about geometric generalizations of combinatorial problems. To understand the limitations of topological techniques one has to study those types of problems, where geometric results deviate considerably from their combinatorial special cases. A central goal will thus be to delimit rigid combinatorial results from their flexible geometric counterparts. In addition to showing the existence of a solution to some combinatorial problem, one is often interested in quantifying how rich the space of solutions is. General topological methods will be developed that provide lower bounds for the topology of the space of solutions of a given combinatorial problem. 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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