13 citations · 67 across the 11 of their papers we have counts for
11 papers
Chambered invariants of real Cauchy-Riemann operators
Aleksander Doan, Thomas Walpuski
Motivated by counting pseudo-holomorphic curves in symplectic Calabi-Yau -folds, this article studies a chamber structure in the space of real Cauchy-Riemann operators on a Riem…
Holomorphic Floer Theory and the Fueter Equation
Aleksander Doan, Semon Rezchikov
We outline a proposal for a -category associated to a hyperkähler manifold , which categorifies the subcategory of the Fukaya category of generated by c…
The Gopakumar-Vafa finiteness conjecture
Aleksander Doan, Eleny-Nicoleta Ionel, Thomas Walpuski
The Gopakumar-Vafa conjecture predicts that the BPS invariants of a symplectic 6-manifold, defined in terms of the Gromov-Witten invariants, are integers and all but finitely many…
Equivariant Brill-Noether theory for elliptic operators and super-rigidity of -holomorphic maps
Aleksander Doan, Thomas Walpuski
The space of Fredholm operators of fixed index is stratified by submanifolds according to the dimension of the kernel. Geometric considerations often lead to questions about the in…
Counting embedded curves in symplectic 6-manifolds
Aleksander Doan, Thomas Walpuski
Based on computations of Pandharipande, Zinger proved that the Gopakumar-Vafa BPS invariants for primitive Calabi-Yau classes and arbitrary Fano classes $…
Castelnuovo's bound and rigidity in almost complex geometry
Aleksander Doan, Thomas Walpuski
This article is concerned with the question of whether an energy bound implies a genus bound for pseudo-holomorphic curves in almost complex manifolds. After reviewing what is know…
On counting associative submanifolds and Seiberg-Witten monopoles
Aleksander Doan, Thomas Walpuski
Building on ideas from [DT98; DS11; Wal17; Hay17], we outline a proposal for constructing Floer homology groups associated with a G2-manifold. These groups are generated by associa…
On the existence of harmonic spinors
Aleksander Doan, Thomas Walpuski
We prove the existence of singular harmonic spinors on -manifolds with . The proof relies on a wall-crossing formula for solutions to the Seiberg-Witten equ…
Deformation theory of the blown-up Seiberg-Witten equation in dimension three
Aleksander Doan, Thomas Walpuski
Associated with every quaternionic representation of a compact, connected Lie group there is a Seiberg-Witten equation in dimension three. The moduli spaces of solutions to these e…
Seiberg-Witten monopoles with multiple spinors on a surface times a circle
Aleksander Doan
The Seiberg-Witten equation with multiple spinors generalises the classical Seiberg-Witten equation in dimension three. In contrast to the classical case, the moduli space of solut…
Adiabatic limits and Kazdan-Warner equations
Aleksander Doan
We study the limiting behaviour of solutions to abelian vortex equations when the volume of the underlying Riemann surface grows to infinity. We prove that the solutions converge s…