SOLNESS: Castles in the air?
HILDA: Yes! Castles in the air — they're so easy to hide away in. And easy to build too.
(Looking contemptuously at him.) Especially for builders who have a dizzy conscience.
— Henrik Ibsen, The Master Builder
Department of Mathematics, Stony Brook University
Stony Brook, NY 11794-3651, USA
office: Math Tower 2-106
email: aleksander dot doan at stonybrook dot edu
I am a fifth year PhD student at Stony Brook University, working under the supervision of Simon Donaldson. Starting from Fall 2019, I will be a Junior Fellow of the Simons Society of Fellows and a Postdoctoral Research Scientist at Columbia University. I will also hold a Junior Research Fellowship at Trinity College, University of Cambridge (on leave in the academic year 2019/2020).
Here is a picture of me; and another one here.
Research summary: a short, non-technical version and an extended version
You can watch me talking about my work here and here.
Equivariant Brill-Noether theory for elliptic operators and super-rigidity of J-holomorphic maps (with T. Walpuski)
preliminary version (2018)
Castelnuovo's bound and rigidity in almost complex geometry (with T. Walpuski)
On counting associative submanifolds and Seiberg-Witten monopoles (with T. Walpuski)
Deformation theory of the blown-up Seiberg-Witten equation in dimension three (with T. Walpuski)
On the existence of harmonic Z2 spinors (with T. Walpuski)
Journal of Differential Geometry (2018) / arXiv:1710.06781
Seiberg-Witten monopoles with multiple spinors on a surface times a circle
Journal of Topology (2018) / arXiv:1701.07942
Adiabatic limits and Kazdan-Warner equations
Calculus of Variations and PDE (2018) / arXiv:1701.07931
Symplectic cohomology for stable fillings
Part III essay on symplectic fillability
Critical points of one-dimensional Gaussian mixtures
Bachelor's thesis on the Picard-Lefschetz theorem (in Polish)
Some of my photos