# CAREER: Geometry of Mapping Class Groups and Surface Bundles

> **NSF 01002930DB NSF RESEARCH & RELATED ACTIVIT** · University of California-Riverside (CA) · $543,918

## Abstract

The mathematics in this research project centers around questions in geometry and topology, which are broadly concerned with understanding various notions of shape. This project focuses on 2-dimensional spaces called surfaces, which are fundamental in many areas of mathematics. Surfaces can be flat, like a piece of paper, or curved, like the outside of a ball, a donut, or a saddle, and the various shapes they take often strongly constrain the shapes of the higher dimensional spaces in which they live. The educational portion of this project involves a variety of activities aimed at recruiting and supporting students into mathematics. The first part continues a series of workshops featuring mini courses by early career speakers on their cutting-edge research aimed at graduate students. The second part establishes a series of undergraduate research and recruitment events connecting undergraduate mathematics researchers with graduate recruiters from programs in the region. The third part is a Topical Pedagogy Seminar which will provide graduate students and postdocs training in incorporating topical material into foundational mathematics courses.

A remarkable and ubiquitous example of this mathematical phenomenon is a surface bundle, which just like a donut, can be sliced so that the cross-sections are surfaces. Unlike a donut, however, as one moves through most surface bundles, the surface cross-sections can twist and deform in complicated ways. This twisting–which essential

## Key facts

- **NSF award ID:** 2441982
- **Awardee organization:** University of California-Riverside (CA)
- **SAM.gov UEI:** MR5QC5FCAVH5
- **PI:** Matthew G Durham
- **Primary program:** 01002930DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** CAREER-Faculty Erly Career Dev
- **Estimated total:** $543,918
- **Funds obligated:** $117,892
- **Transaction type:** Continuing Grant
- **Period:** 07/01/2025 → 04/30/2026

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2441982

## Citation

> US National Science Foundation, Award 2441982, CAREER: Geometry of Mapping Class Groups and Surface Bundles. Retrieved via AI Analytics 2026-06-06 from https://api.ai-analytics.org/grant/nsf/2441982. Licensed CC0.

---

*[NSF Awards dataset](/datasets/nsf-awards) · CC0 1.0*