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


Aleksander Doan

Department of Mathematics, Columbia University
2990 Broadway, New York, NY 10027, USA

office: 627
email: aleksander.doan@columbia.edu


I am a Junior Fellow of the Simons Society of Fellows and a Postdoctoral Research Scientist at Columbia University, a position held in conjunction with a Junior Research Fellowship at Trinity College, University of Cambridge. I completed my PhD in 2019 at Stony Brook University, supervised by Simon Donaldson. Here is a picture of me; and another one here.

Curriculum Vitae



Teaching

Spring 2021: Ordinary Differential Equations (MATH 2030)



Research interests

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

Recordings of some of my talks: Institute for Advanced Study, Simons Center, Simons Collaboration on Special Holonomy

In this short interview published by the Simons Foundation I talk about topology and my work in non-technical terms.



Papers

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)
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



PhD Dissertation

Monopoles and Fueter sections on three-manifolds (2019)

My PhD dissertation at Stony Brook University. It incorporates some of the material from my first five papers, three of which were written in collaboration with Thomas Walpuski. The introduction is a short survey of generalized Seiberg-Witten equations, Fueter sections, and their relation to gauge theory in higher dimensions.



Other

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)


Some of my photos