Trinity College

Cambridge, CB2 1TQ

United Kingdom

aqd20@cam.ac.uk

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

In September, I will join University College London as a Lecturer in Pure Mathematics. I will spend Fall 2022 as a Research Member in the MSRI program *Analytic and Geometric Aspects of Gauge Theory* in Berkeley.

*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

arXiv:2006.01352 (2020)

*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 (2020) / arXiv:1809.04731

*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

*On the existence of harmonic Z _{2} spinors* — with T. Walpuski

Journal of Differential Geometry (2019) / arXiv:1710.06781

*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

*Monopoles and Fueter sections on three-manifolds*

PhD dissertation at Stony Brook University (2019)

*Holomorphic Floer theory and the Fueter equation*,
Institute for Advanced Study, 2022

*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

Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics, four talks on gauge theory

Simons Center for Geometry and Physics, three talks on gauge theory

*Beyond squares and triangles*,
general audience interview published by the Simons Foundation, 2020