Conference: St. Louis Topology Conference: Flows and Foliations in 3-Manifolds

Saint Louis University, Saint Louis MO

Investigators

Abstract

This award provides participant support for the St. Louis Topology Conference taking place May 17-19, 2024 in St. Louis, Missouri, USA. The theme of the conference is Flows and Foliations in 3-manifolds. The mathematical concept of a dynamical system allows for any continuously time-varying physical system to be considered within a uniform framework, as a “state space” that organizes all possible instantaneous configurations, together with a “flow” that describes the evolution of states with time. The conference is focused on the way that the geometry and topology of a space interacts with the kinds of dynamical systems that it supports, with an eye towards applications in dynamics, geometry, and topology. The organizers are committed to broad recruitment across a diverse set of students and postdoctoral researchers. In addition to hour-long lectures by established researchers, there will be lightning talks as well as a panel discussion on issues faced by early career mathematicians. Flows and foliations in three dimensional manifolds can be fruitfully viewed through many lenses, as they stand at the intersection of dynamics, topology, and geometry. Interest in this general area has accelerated since Agol's resolution of the Virtual Fibering Conjecture, with researchers using a variety of tools and ideas such as (pseudo-) Anosov and partially hyperbolic flows, sutured manifold hierarchies, geometric group theory, contact geometry, Floer theory, veering triangulations, and the so-called big mapping class group to study a variety of questions. These include among others the L-space conjecture, the Cannon Conjecture, the Pseudo-Anosov Finiteness Conjecture, and the classification of infinite-type mapping classes. Recent conferences have tended to focus on small subsets of these topics and techniques, and there is a need for an event at which researchers with expertise in these different topics can meet and share their knowledge. Talks will take place at Washington University. The conference website is https://sites.google.com/view/stltc/home. 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.