Research

I am primarily interested in numbers and the geometry of numbers in a broad sense: using pattern recognition, computational geometry, computer algebra, commutative algebra, lattice theory, convex geometry, and combinatorial methods in problems arising in enumerative geometry, moduli theory, and number theory. 

I am also interested in applying tools from derived categories, Bridgeland stability conditions, derived algebraic geometry, differential geometry, and geometric analysis to understand geometric and enumerative aspects of moduli spaces.

Research students

• Alexia Ascott, University of Cambridge.

• Owen Mackenzie, University of Cambridge.

• Zhichen Zhou, University of Cambridge.

Publication/Preprint

• A proof of the Briançon-Iarrobino Conjecture in three dimensions, with O. Mackenzie. 

• A conjectural generalization of the Briançon-Iarrobino Conjecture, with A. Ascott and Z. Zhou.

• An obstruction to smoothing stable maps, with M. Swaminathan. Submitted

• Constructing smoothings of stable maps, arXiv, with M. Swaminathan.  Advances in Mathematics. Volume 467, no. 110188.  2025.

• Conjectural criteria for the most singular points of the Hilbert schemes of points . Experimental Mathematics, 1–16, 2024.

• An interesting wall-crossing: Failure of the wall-crossing/MMP correspondence, arXiv.  Selecta Mathematica New Series, Volume 30, Number 102, 2024. 

• Geometry of canonical genus four curves, arXiv.  Proceedings of the London Mathematical Society, Volume 128, Issue 1, 2024.

• The desingularization of the theta divisor of a cubic threefold as a moduli space ,  arXiv, with A. Bayer, S. Beentjes, S. Feyzbakhsh, G. Hein, D. Martinelli, B. Schmidt.  Geometry & Topology, Volume 28, Issue 1, 2024.

• Wall-crossing and birational geometry, a survey to appear in the Proceedings of Nottingham Algebraic Geometry Seminar.

• Wall-crossing pathologies in three dimensions, a survey to appear in ZAG Handbook of Modern Algebraic Geometry.

Teaching/Supervision

• Part III Homological Algebra: Lecturer, Lent  2026, University of Cambridge.

• Summer Research Program supervision, 2025, University of Cambridge.

• Summer Research Program supervision, 2024, University of Cambridge.

• Part III Essay supervision, 2023-2024, University of Cambridge.

• Part II Riemann Surfaces:  Supervisor, Fall (Michaelmas term) 2023, Clare College, University of Cambridge.

• Engineering Mathematics/Mathematics for Natural Sciences: (co-)Lecturer, Spring 2022, University of Edinburgh.

• Accelerated Algebra and Calculus for Direct Entry: (co-)Lecturer, Fall 2021, University of Edinburgh.

• Fundamentals of Pure Mathematics: Tutor, Spring 2020, University of Edinburgh.

• Honours Algebra (Skills): Tutor, Spring 2020, University of Edinburgh.

• Commutative Algebra: Tutor, Fall 2019, University of Edinburgh.

• Combinatorics and Graph Theory: Tutor, Fall 2019, University of Edinburgh.

• Facets of mathematics : Tutor, Fall 2018, University of Edinburgh,

• Proofs and problem solving: Tutor, Spring 2018, University of Edinburgh,

• Honours algebra: Tutor, Spring 2018, University of Edinburgh,

• Introduction to linear Algebra:  Tutor, Fall 2018, University of Edinburgh,

Other activities

• Organiser of seminars on derived categories, stability and applications, Spring/Summer 2021, Loughborough University,

• Co-organiser of the Graduate Student Seminar, Spring 2019, MSRI, Berkeley,

• Organiser of the arXiv review seminar in algebraic geometry, Fall 2017, University of Edinburgh,