Knots in Dynamical Systems
BSU Mathematics Seminar — Fall 2025
- When
- Monday, November 24, 2025 • 3:00–4:00 PM
- Where
- DMF 461, Bridgewater State University
- Speaker
- Solly Coles (Tufts University)
- Format
- In-person. A/V needs: TBD per speaker. Zoom/Recording: TBD.
- Organizers
-
Vignon Oussa (VOUSSA@bridgew.edu) •
Xiangfei “Fei” Chen (X10CHEN@bridgew.edu) •
Mahmoud El-Hashash (MELHASHASH@bridgew.edu)
Abstract
Given a flow in 3 dimensional space, the path traced out by a periodic point can be thought of as a knot (an embedded circle in the space). In this talk, we will discuss the kinds of knots (up to isotopy) that can appear in this way, and see how a knot-theoretic viewpoint can help to quantify the tangled-ness of orbits. Some of these problems can be translated into the language of ergodic theory, which proves especially useful when the flow is chaotic.
We will mainly focus on Smale’s Axiom A flows, which generalise geodesic flows over hyperbolic surfaces. These systems have infinitely many periodic orbits, the number of which grows exponentially fast with the length. Ergodic methods allow us to understand how the periodic orbits are distributed throughout the space, which is key for answering questions such as: On average, what is the linking number of a pair of orbits?
Short Bio
Solly Coles is a Norbert Wiener Postdoctoral Fellow at Tufts University, working with
Boris Hasselblatt. His research is in hyperbolic dynamics and its interactions with
low-dimensional geometry and topology.
Questions? Contact an organizer:
Vignon Oussa,
Xiangfei (Fei) Chen,
Mahmoud El-Hashash.