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.

photo

Research


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 Z2 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)

Some of my talks


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

Teaching


Ordinary Differential Equations (MATH 2030, Spring 2021)

Course evaluations 2014—2021

Top