I am a second-year PhD student supervised by Saul Schleimer. My research interests include low-dimensional topology, geometry, and dynamical systems, especially the rich interactions between these fields. Within this, I am currently interested in the relationship between pseudo-Anosov flows on 3-manifolds and veering triangulations.

Papers

• Recognising perfect fits. In Preparation.
• "Classification of partially hyperbolic surface endomorphisms" with Andy Hammerlindl, in Geometriae Dedicata 216.3 (2022): 29.
• "Dynamically incoherent surface endomorphisms" with Andy Hammerlindl, in Journal of Dynamics and Differential Equations (2022): 1-13.
• "Partially hyperbolic surface endomorphisms" with Andy Hammerlindl, in Ergodic Theory and Dynamical Systems 41.1 (2021): 272-282.

Talks

• "Between chaotic flows and combinatorics" at the Warwick Mathematics Postgraduate Seminar, 2023
• "Modular links and their complements" at GT GAPS (online), 2023
• "Knotted orbits of flows" at the Warwick Mathematics Postgraduate Seminar, 2022
  
• "Complements of dynamical knots" at the Monash Topology Seminar, 2022
• "Classification of partially hyperbolic surface endomorphisms" at the PKU Dynamical Systems Seminar, Peking University (online), 2021
• "Partially hyperbolic surface endomorphisms" at the Monash Topology Seminar, 2018

History

Before Warwick, I completed my MSc at the University of Melbourne and earlier completed my Honours degree at Monash University. My MSc thesis was supervised by Craig Hodgson; I studied the complements of periodic orbits of flows on 3-manifolds, especially the modular flow. While at Monash, I studied the dynamics of non-invertible surface maps under the supervision of Andy Hammerlindl. I continued to work with Andy as a research assistant, extending the work from this thesis. We ended up classifying partially hyperbolic surface endomorphisms, contained within the papers above.

Contact

e-mail: layne.hall@warwick.ac.uk