Conference: 1, 2, 3: Curves, Surfaces, and 3-Manifolds

William Marsh Rice University, Houston TX

Investigators

Abstract

This NSF award provides partial support for U.S. based participants of a conference titled "1, 2, 3; Curves, Surfaces, and 3-Manifolds" in Nahsholim Israel and the Technion Institute of Technology, May 7-11, 2023. The goal of the conference is to bring together researchers at all career stages to discuss intersections in geometry and topology in dimensions 1, 2, and 3. These topics have become intimately intertwined over the past 40 years, and have provided the impetus for the much of the development of entire fields of mathematics, such as geometric group theory. Importantly, the conference will also include workshop-style talks aimed at helping bridge the gap between seasoned researchers and the next generation of mathematicians. The confluence of topology and geometry of three dimensional manifolds, and the geometric properties of mapping class groups, has been intensively studied over the last several decades and is of central importance in a variety of mathematical disciplines. For example, hyperbolic 3-manifolds are often governed by certain surfaces contained in them. These surfaces inherit their own hyperbolic structures from their inclusion into the 3-manifold, and these structures are very coarsely encoded by collections of curves on the surface. Miraculously, in key situations, the hyperbolic 3-manifold can be reconstituted from this collection of curves--this is the essential content of the Ending Lamination Theorem. The mathematics developed to study curves used in the proof of this theorem simultaneously provide a powerful toolkit for studying mapping class groups of surfaces. Abstractions of these tools now provide the framework for studying a very large and robust class of groups from a geometric perspective. More details can be found on the conference website: https://cms-math.net.technion.ac.il/123-curves-surfaces-and-3-manifolds/ This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.