# LEAPS-MPS: Examination of knot invariants via computational methods

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · Duquesne University (PA) · $249,941

## Abstract

This project investigates knot theory; a field of mathematics concerned with understanding how loops (like knots in a string) can be embedded and manipulated in three-dimensional space. Knot theory is part of the broader area of topology, which studies the properties of shapes that remain unchanged when stretched or bent. While abstract in nature, knot theory plays a role in many scientific domains: molecular biology (where it helps explain DNA folding), physics (in the study of quantum entanglement), and computer science (in data analysis). The research will focus on mathematical objects called invariants: quantities or properties that remain unchanged when a knot is deformed in specific ways. These are crucial tools for distinguishing between different types of knots and understanding their structure. The project aims to uncover new patterns, propose novel tools for identification for certain families of knots, and push the boundaries of what is computationally accessible in topology.  To advance this work, the project incorporates machine learning, a form of artificial intelligence where computers detect patterns in data, and predictive modeling, which uses data to make statistically informed guesses about unknown or complex systems.  In addition, the PI will involve undergraduate students in active research and departmental programs, create computational packages to support further exploration, and engage with K–12 communities through outreach programs. 
 
This work con

## Key facts

- **NSF award ID:** 2532488
- **Awardee organization:** Duquesne University (PA)
- **SAM.gov UEI:** NGYSJ2L1LZX3
- **PI:** Samantha Allen
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** Harnessing the Data Revolution, Machine Learning Theory
- **Estimated total:** $249,941
- **Funds obligated:** $249,941
- **Transaction type:** Standard Grant
- **Period:** 09/01/2025 → 08/31/2027

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2532488

## Citation

> US National Science Foundation, Award 2532488, LEAPS-MPS: Examination of knot invariants via computational methods. Retrieved via AI Analytics 2026-06-08 from https://api.ai-analytics.org/grant/nsf/2532488. Licensed CC0.

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