Aleksander Doan

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 the State University of New York in Stony Brook, working under the supervision of Simon Donaldson. I plan to graduate in the summer of 2019. My research focuses on gauge theory, manifolds with special holonomy, symplectic geometry, and low-dimensional topology.

Here is a picture of me; and another one here.

Curriculum Vitae

Research summary: a short, non-technical version and an extended version


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)
arXiv:1809.04731 (2018)

On counting associative submanifolds and Seiberg-Witten monopoles (with T. Walpuski)
arXiv:1712.08383 (2017)

Deformation theory of the blown-up Seiberg-Witten equation in dimension three (with T. Walpuski)
arXiv:1704.02954 (2017)

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


Undergraduate projects:
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)

Symplectic Geometry Reading Seminar

Reading Seminar on the Kapustin-Witten Equations

Some of my photos