# CAREER: Mathematical Aspects of Topological Phases

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · University of Washington (WA) · $514,281

## Abstract

Developing innovative materials with revolutionary properties is at the forefront of modern research. This project focuses on topological phases of matter, a novel class of materials that conduct electricity along their edges in a way that remains unaffected by defects or noise. This makes them ideal to improve quantum computations - which are notoriously sensitive to noise. This project aims to stimulate innovations in quantum technology by unlocking a deeper understanding of how electrons behave in these materials. The project investigates how stable currents emerge between topologically distinct phases; compute their profile and their speed; and derive effective equations for their propagation. The educational component of this project seeks to inspire students by emphasizing the vital role of mathematical skills in today's professional landscape. The Principal Investigator (PI) plans to organize a monthly talk series, "Y Math?", which features industry leaders showcasing how mathematics drives innovation across diverse fields. 

The first research track of this project focuses on topological insulators, materials whose Hamiltonians have a spectral gap and a topologically non-trivial Fermi projector. For straight interfaces, the bulk-edge correspondence predicts that the conductance along an interface between insulating phases of matter is equal to the Hall conductance jump across the interface. The PI seeks to extend this principle to curved interfaces by extracting fr

## Key facts

- **NSF award ID:** 2439949
- **Awardee organization:** University of Washington (WA)
- **SAM.gov UEI:** HD1WMN6945W6
- **PI:** Alexis Drouot
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** QUANTUM COMPUTING, CAREER-Faculty Erly Career Dev
- **Estimated total:** $514,281
- **Funds obligated:** $108,010
- **Transaction type:** Continuing Grant
- **Period:** 07/01/2025 → 06/30/2030

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2439949

## Citation

> US National Science Foundation, Award 2439949, CAREER: Mathematical Aspects of Topological Phases. Retrieved via AI Analytics 2026-06-06 from https://api.ai-analytics.org/grant/nsf/2439949. Licensed CC0.

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