Research

My research lies within the field of algebraic dynamics, the study of iterated maps on spaces which are defined algebraically. I am especially interested in rational self-maps of varieties (complex dynamics), particularly in higher dimensions, and exploring their connection with non-Archimedean geometry. Often I am concerned with the notions surrounding dynamical complexity such as dynamical degrees, algebraic stability, and modifying surfaces to better understand these.

Works

Rational Inner Skew Products
In preparation with Alan Sola, Jazmin Raissy, Liz Vivas
Classification of Rational Maps on an Elliptic Surface
In preparation with Giacomo Mezzedimi.
The Calculus of Blowups on a Ruled Surface
In final preparation.
Algebraic Stability for Rational Skew Products on a Surface.
Preprint available on arXiv.
Skew Products on the Berkovich Projective Line
Preprint available on arXiv.
On the Stabilisation of Rational Surface Maps
To appear.
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 34 (2025) no. 1, pp. 47-74

Talks and Travel

AMS Spring Central Sectional Meeting, March 2025
Special Session: Current Trends in Complex Dynamics
TBD

Birational Geometry and Dynamics, SwissMAP Research Station, July 2024

AMS Spring Central Sectional Meeting, April 2024
Special Session: Panorama of Holomorphic Dynamics
Rational Maps and the Calculus of Blowups

Dynamics Seminar, The Ohio State University, 28th March 2024
Algebraic Stability and Rational Maps on a Surface

Joint Mathematics Meeting, Boston, January 2023
AMS Special Session on Recent Advances in Arithmetic Dynamics I
Skew Products on the Berkovich Projective Line

Algebra Seminar, Pennsylvania State University, 8th December 2022
Non-Ideal Algebraic Geometry with Berkovich Space

Midwest Dynamical Systems Conference, 18th-20th November 2022
The Dynamics of Rational Skew Products

Dynamics Seminar, University of Michigan, 24th October 2022
Algebraic Stability and Skew Products

Workshop in Arithmetic and Algebraic Dynamics, Harvard, May 2022
The Dynamics of Rational Skew Products

Dynamical Systems Seminar, IUPUI, 18th November 2021
Stabilising Birational Surface Maps