I am a Lecturer in Pure Mathematics at University College London and a Junior Research Fellow of Trinity College, Cambridge. My research areas are differential geometry, gauge theory, and symplectic topology.

London office: Room 346, Kathleen Lonsdale Building, UCL
Cambridge office: Room D017, Centre for Mathematical Sciences

Postal address: Trinity College, Cambridge, CB2 1TQ
Email: a.doan@ucl.ac.uk



Holomorphic Floer theory and the Fueter equation — with S. Rezchikov
arXiv:2210.12047 (2022)

The Gopakumar-Vafa finiteness conjecture — with E. Ionel and T. Walpuski
arXiv:2103.08221 (2021)

Equivariant Brill-Noether theory for elliptic operators and super-rigidity of J-holomorphic maps — with T. Walpuski
Forum of Mathematics, Sigma (2023) / arXiv:2006.01352

Counting embedded curves in symplectic 6-manifolds — with T. Walpuski
Comentarii Mathematici Helvetici (2022) / arXiv:1910.12338 (2019)

Castelnuovo's bound and rigidity in almost complex geometry — with T. Walpuski
Advances in Mathematics (2021) / arXiv:1809.04731

On the existence of harmonic Z2 spinors — with T. Walpuski
Journal of Differential Geometry (2021) / arXiv:1710.06781

Deformation theory of the blown-up Seiberg-Witten equation in dimension three — with T. Walpuski
Selecta Mathematica (2020) / arXiv:1704.02954

On counting associative submanifolds and Seiberg-Witten monopoles — with T. Walpuski
Pure and Applied Mathematics Quarterly (2019) / arXiv:1712.08383

Seiberg-Witten monopoles with multiple spinors on a surface times a circle
Journal of Topology (2019) / arXiv:1701.07942

Adiabatic limits and Kazdan-Warner equations
Calculus of Variations and PDE (2018) / arXiv:1701.07931

Analytic and algebraic aspects of gauge theory
Overview article for the MSRI research program (2022), design and typesetting by The Emissary

Beyond squares and triangles
General audience interview published by the Simons Foundation (2020)

Monopoles and Fueter sections on three-manifolds
PhD dissertation at Stony Brook University (2019)

Some of my talks

Holomorphic Floer theory and the Fueter equation, New Four-Dimensional Gauge Theories, 2022
see also similar talks at the Institute for Advanced Study and M-Seminar

Equivariant transversality meets geometric measure theory, Western Hemisphere Virtual Symplectic Seminar, 2021

Counting pseudo-holomorphic curves in symplectic six-manifolds, Gauge Theory Virtual Seminar, 2021

Counting embedded curves in symplectic six-manifolds, Institute for Advanced Study, 2020

From curve counting to gauge theory, Oxford–London Gauge Assembly, 2020

On complexification and categorification, Geometry and Analysis of Moduli Spaces, 2020

From gauge theory to calibrated geometry and back, Simons Collaboration on Special Holonomy, 2019

The ADHM vortex equations on Riemann surfaces, Novel Vistas on Vortices, 2019

Multiple covers of associatives and ADHM monopoles, Gauge Theory and Special Holonomy, 2018

Fueter sections and wall-crossing in Seiberg-Witten theory, Special Holonomy: Progress and Open Problems, 2017

Seiberg-Witten monopoles with multiple spinors on a surface times a circle, Recent Developments in Gauge Theory, 2016


Ordinary Differential Equations (MATH 2030, Spring 2021)

Course evaluations 2014—2021