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 fourth year PhD student at the State University of New York in Stony Brook, working under the supervision of Simon Donaldson. My research focuses on mathematical gauge theory and Riemannian manifolds with special holonomy. Here is my CV and a picture of me.



Research

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)

Seiberg-Witten monopoles with multiple spinors on a surface times a circle
arXiv:1701.07942 (2017)

On the existence of harmonic Z2 spinors (with T. Walpuski)
arXiv:1710.06781 (2017), to appear in Journal of Differential Geometry

Adiabatic limits and Kazdan-Warner equations
arXiv:1701.07931 (2017), to appear in Calculus of Variations and PDE



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)


Symplectic Geometry Reading Seminar

Some of my photos