# Quantitative Symplectic Geometry in Higher Dimensions

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · University of Southern California (CA) · $300,000

## Abstract

Abstract:

Symplectic geometry is a branch of modern mathematics which lies at the interface of many areas in modern geometry and theoretical physics. Among other things, it can be used to place subtle and surprising restrictions on the dynamics of a broad class of systems (think motions of celestial bodies or the molecules in a gas). Understanding the scope of these restrictions and how to effectively utilize them in naturally arising physical systems is an exciting active area of research. In this project, the PI will develop new tools and paradigms to study the quantitative side of symplectic geometry. The PI will also initiate the study of "digital symplectic geometry", which aims to link deep geometric tools with numerical simulations and methods from machine learning. In addition, the PI will also be actively involved in various community-building and mentorship activities, including organizing intensive learning retreats for the wider Southern California geometry and topology community and mentoring undergraduates in research projects at the interface of pure and applied mathematics.

In more detail, a central theme is to develop filtered refinements and higher extensions of powerful emerging tools from pseudoholomorphic curve theory (symplectic field theory, Floer homology, Gromov–Witten invariants, Fukaya categories, ...) in order to systematically investigate rigidity and flexibility properties of Hamiltonian flows. Along the way, this project will explore new t

## Key facts

- **NSF award ID:** 2506639
- **Awardee organization:** University of Southern California (CA)
- **SAM.gov UEI:** G88KLJR3KYT5
- **PI:** Kyler B Siegel
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** —
- **Estimated total:** $300,000
- **Funds obligated:** $300,000
- **Transaction type:** Standard Grant
- **Period:** 06/15/2025 → 05/31/2028

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2506639

## Citation

> US National Science Foundation, Award 2506639, Quantitative Symplectic Geometry in Higher Dimensions. Retrieved via AI Analytics 2026-07-26 from https://api.ai-analytics.org/grant/nsf/2506639. Licensed CC0.

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