# CAREER: Algebra and Representation Theory for Non-Semisimple Topological Field Theory

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · Utah State University (UT) · $450,000

## Abstract

This award will support research in the field of algebra and representation theory with connections to theoretical physics. Representation theory is the branch of mathematics concerned with the study of symmetry using techniques from linear algebra, such as vectors and matrices. Classical examples of symmetry include rotations of a circle and reflections of a square. Modern research in mathematics naturally encounters more abstract notions of symmetry and requires the development of more advanced techniques for their study. The PI will identify and study concrete instances of these abstract symmetries and apply the results to advance the mathematical understanding of quantum field theory in dimensions two and three. The research will also develop new connections between algebra, representation theory, and low dimensional topology. This project integrates education, research, and career training opportunities for high school, undergraduate, and graduate students. Examples include creating a series of videos which will improve the algebra education of Utah's high school mathematics teachers-in-training, and organizing the graduate student focused Moab Topology Conference.

In more detail, the PI will engage in three related research projects. Each project is motivated by and has direct implications for the long-standing conjecture that Rozansky-Witten theory, a three dimensional supersymmetric quantum field theory, defines a non-semisimple topological field theory. In the fi

## Key facts

- **NSF award ID:** 2440471
- **Awardee organization:** Utah State University (UT)
- **SAM.gov UEI:** SPE2YDWHDYU4
- **PI:** Matthew B Young
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** CAREER-Faculty Erly Career Dev
- **Estimated total:** $450,000
- **Funds obligated:** $281,548
- **Transaction type:** Continuing Grant
- **Period:** 09/01/2025 → 08/31/2030

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2440471

## Citation

> US National Science Foundation, Award 2440471, CAREER: Algebra and Representation Theory for Non-Semisimple Topological Field Theory. Retrieved via AI Analytics 2026-06-08 from https://api.ai-analytics.org/grant/nsf/2440471. Licensed CC0.

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