# Microlocal Analysis and Wave Phenomena in Geometric Settings

> **NSF 01002627DB NSF RESEARCH & RELATED ACTIVIT** · Stanford University (CA) · $199,999

## Abstract

This award supports the development and applications of methods in the field of microlocal analysis. Roughly speaking, this field keeps track of the position and frequency, or momentum, of waves (or more generally, functions, such as the amplitudes and phases of waves) simultaneously. The planned applications, such as the analysis of long-time or far field behavior, are to wave propagation and other related phenomena such as quantum fields on curved spaces; curvature of the space itself is a feature of mathematical general relativity. Although the project concerns their mathematical theory, these problems are closely connected to the physical world. Wave propagation is ubiquitous in nature, with light and gravitational waves being important examples, and the latter (gravitation) giving rise to curved spacetimes. Scattering theory of quantum particles is another subject governed by microlocal analysis: these aspects enter into the description of quantum waves at large distances. Many of the projects are suitable for research by doctoral students, and the Principal Investigator (PI) strives to contribute to the education of a new generation of mathematicians and scientists.

Some of the projects describe the long-time or far field behavior, including existence, of waves, such as electromagnetic or gravitational waves, on curved spacetimes. The microlocal approach to analysis on these spaces has made breakthroughs possible in the PI's (in part collaborative) work on linear an

## Key facts

- **NSF award ID:** 2553664
- **Awardee organization:** Stanford University (CA)
- **SAM.gov UEI:** HJD6G4D6TJY5
- **PI:** Andras Vasy
- **Primary program:** 01002627DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** —
- **Estimated total:** $199,999
- **Funds obligated:** $199,999
- **Transaction type:** Standard Grant
- **Period:** 07/01/2026 → 06/30/2028

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2553664

## Citation

> US National Science Foundation, Award 2553664, Microlocal Analysis and Wave Phenomena in Geometric Settings. Retrieved via AI Analytics 2026-06-07 from https://api.ai-analytics.org/grant/nsf/2553664. Licensed CC0.

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