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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:
  • Olya Mandelshtam
  • (401) 863-1867
  • olya@math.brown.edu
Award Date:06/01/2020
Estimated Total Award Amount: $ 168,067
Funds Obligated to Date: $ 168,067
  • FY 2020=$168,067
Start Date:07/01/2020
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:Combinatorics of Interacting Particles and Applications
Federal Award ID Number:1953891
DUNS ID:001785542
Parent DUNS ID:001785542
Program:Combinatorics
Program Officer:
  • Stefaan De Winter
  • (703) 292-2599
  • sgdewint@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

The proposed project explores structures that lie at the intersection of combinatorics, representation theory, statistical physics, and integrable systems. The proposed research also has many applications: the key object of this work, the asymmetric simple exclusion process (ASEP), has been studied as a model for traffic flow, as well as in biological processes such as translation in protein synthesis and kinetic biopolymerization. In the longer term, the proposed project has the potential to have an important impact on these applications. Some of the topics of the proposed project are accessible to younger researchers, with several projects intended for work with students. Workshop organization, outreach, and activities aimed at improving climate in STEM are also planned. This project is jointly funded by the Combinatorics program and the Established Program to Stimulate Competitive Research (EPSCoR). The principal goal of this project is to study the remarkable connection between particle models such as ASEP and orthogonal polynomials. The first part of this work concerns Macdonald polynomials of type A as an application of the combinatorics of the ASEP on a circle, through recently discovered formulas that use multiline queues to connect probabilities of the ASEP to symmetric and nonsymmetric Macdonald polynomials. It is proposed to use those new formulas to explore Schur positivity of modified Macdonald polynomials: one line of attack is to study the quasisymmetric Macdonald polynomial. The second part of this project concerns the extension of the results obtained for Macdonald polynomials of type A to the type BC setting to discover formulas both for Koornwinder polynomials and probabilities of the multispecies ASEP with open boundaries. Thus far such formulas exist only for the two-species ASEP case corresponding to a special case of Koornwinder polynomials, studied in earlier works. It is proposed to merge those results with the multiline queue approach to find a new object that incorporates boundary conditions and admits any number of species. 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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