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)
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