NSF award 2603897 · University of Pennsylvania

Letter braiding invariants of words in fundamental groups and arithmetic

Final report due

28 November 2029

in 1,137 days · The award ends on 31 July 2029.

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Decide about an extension2 Apr 2029in 897 days
award ending 2029-07-31 · Research.gov
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Extension request16 Jun 2029in 972 days
award ending 2029-07-31 · Research.gov
PAPPG 24-1: “at least 45 days prior to the end date”
No-cost extension notice21 Jul 2029in 1007 days
award ending 2029-07-31 · Research.gov
PAPPG 24-1: “at least ten calendar days prior to the end date”
Final report due28 Nov 2029in 1137 days
award ending 2029-07-31 · Research.gov
PAPPG 24-1: “no later than 120-days following the end date of the award”
Project outcomes report due28 Nov 2029in 1137 days
award ending 2029-07-31 · Research.gov
PAPPG 24-1: “no later than 120 days following the end date”
Award is closed out28 Nov 2029in 1137 days
award ending 2029-07-31 · Research.gov
PAPPG 24-1: “financially closed out 120 days after their expiration date”

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NSF lists this award's end date as 31 July 2029.
NSF rules say the final report is due no later than 120 days after that.
So the final report is due by 28 November 2029.

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Award card

Award number: 2603897
Period of support: 15 Aug 2026 – 31 Jul 2029
Amount: $199,984
Awardee: University of Pennsylvania, Philadelphia, PA
Program: TOPOLOGY
Directorate: MPS

Abstract

This project will study algebraic objects with varied applications, such as ones representing paths along some physical surface or solutions to polynomial equations. The approach proceeds by analyzing strings of letters that record the essential complexity of the object, through the ways in which those letters interleave. Some of the deepest ideas of mathematics, collectively known as Galois theory, give concrete…

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