Thomas Walpuski

activity

20102026

most citedA compactness theorem for the Seiberg-Witten equation with multiple spinors in dimension three

29 citations · 264 across the 24 of their papers we have counts for

collaborators

24 papers

math.DG2026

The universal moduli space of non-degenerate $Z /2 Z$ harmonic spinors

Siqi He, Gregory J. Parker, Thomas Walpuski

This article equips the universal moduli spaces of non-degenerate $Z /2 Z$ harmonic spinors and eigenspinors with tame Fréchet manifold structures and proves that t…

math.DG2025

Dirac operators twisted by ramified Euclidean line bundles

Gorapada Bera, Thomas Walpuski

This article is concerned with the analysis of Dirac operators $D$ twisted by ramified Euclidean line bundles $(Z, l)$ -motivated by their relation with harmonic $\mathbf{…

math.DG2024

Chambered invariants of real Cauchy-Riemann operators

Aleksander Doan, Thomas Walpuski

Motivated by counting pseudo-holomorphic curves in symplectic Calabi-Yau $3$ -folds, this article studies a chamber structure in the space of real Cauchy-Riemann operators on a Riem…

math.DG2022

Associative submanifolds in Joyce's generalised Kummer constructions

Shubham Dwivedi, Daniel Platt, Thomas Walpuski

This article constructs examples of associative submanifolds in $G_{2}$ -manifolds obtained by resolving $G_{2}$ -orbifolds using Joyce's generalised Kummer construction. As the $G_{2}$ -ma…

math.SG2021★ 6 cited

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…

math.DG2020★ 2 cited

Equivariant Brill-Noether theory for elliptic operators and super-rigidity of $J$ -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…

math.SG2019★ 9 cited

Counting embedded curves in symplectic 6-manifolds

Aleksander Doan, Thomas Walpuski

Based on computations of Pandharipande, Zinger proved that the Gopakumar-Vafa BPS invariants $BPS_{A, g} (X, ω)$ for primitive Calabi-Yau classes and arbitrary Fano classes $…

math.DG2019★ 8 cited

On the compactness problem for a family of generalized Seiberg-Witten equations in dimension three

Thomas Walpuski, Boyu Zhang

We prove an abstract compactness theorem for a family of generalized Seiberg-Witten equations in dimension three. This result recovers Taubes' compactness theorem for stable flat $…

math.DG2018★ 5 cited

Hecke modifications of Higgs bundles and the extended Bogomolny equation

Siqi He, Thomas Walpuski

We establish a Kobayashi-Hitchin correspondence between solutions of the extended Bogomolny equation with a Dirac type singularity and Hecke modifications of Higgs bundles. This co…

math.SG2018★ 9 cited

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…

math.DG2017★ 13 cited

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…

math.DG2017★ 5 cited

On the existence of harmonic $Z_{2}$ spinors

Aleksander Doan, Thomas Walpuski

We prove the existence of singular harmonic $Z_{2}$ spinors on $3$ -manifolds with $b_{1} > 1$ . The proof relies on a wall-crossing formula for solutions to the Seiberg-Witten equ…

math.DG2017★ 10 cited

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…

math.DG2016★ 6 cited

Tangent cones of Hermitian Yang-Mills connections with isolated singularities

Adam Jacob, Henrique Sá Earp, Thomas Walpuski

We give a simple direct proof of uniqueness of tangent cones for singular projectively Hermitian Yang-Mills connections on reflexive sheaves at isolated singularities modelled on $…

math.DG2016★ 16 cited

Hermitian Yang-Mills metrics on reflexive sheaves over asymptotically cylindrical Kähler manifolds

Adam Jacob, Thomas Walpuski

We prove an analogue of the Donaldson-Uhlenbeck-Yau theorem for asymptotically cylindrical Kähler manifolds: If $E$ is a reflexive sheaf over an ACyl Kähler manifold, whi…

math.DG2015★ 14 cited

A compactness theorem for Fueter sections

Thomas Walpuski

We prove that a sequence of Fueter sections of a bundle of compact hyperkahler manifolds $X$ over a $3$ -manifold $M$ with bounded energy converges (after passing to a sub…

math.DG2015★ 21 cited

$G_{2}$ -instantons over twisted connected sums: an example

Thomas Walpuski

Using earlier work of Sá Earp and the author [SEW13] we construct an irreducible unobstructed $G_{2}$ -instanton on an $SO (3)$ -bundle over a twisted connected sum recently di…

math.DG2014★ 9 cited

Spin(7)-instantons, Cayley submanifolds, and Fueter sections

Thomas Walpuski

We prove an existence theorem for Spin(7)-instantons, which are highly concentrated near a Cayley submanifold; thus giving a partial converse to Tian's foundational compactness the…

math.DG2014★ 29 cited

A compactness theorem for the Seiberg-Witten equation with multiple spinors in dimension three

Andriy Haydys, Thomas Walpuski

We prove that a sequence of solutions of the Seiberg-Witten equation with multiple spinors in dimension three can degenerate only by converging (after rescaling) to a Fueter sectio…

math.DG2013★ 27 cited

$G_{2}$ -instantons on twisted connected sums

Henrique Sá Earp, Thomas Walpuski

We introduce a method to construct $G_{2}$ -instantons over compact $G_{2}$ -manifolds arising as the twisted connected sum of a matching pair of building blocks [Kov03,KL11,CHNP12]. Our…

math.DG2012★ 5 cited

Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three

Anda Degeratu, Thomas Walpuski

For $G$ a finite subgroup of $SL (3, C)$ acting freely on $C^{3} ∖ {0}$ a crepant resolution of the Calabi-Yau orbifold $C^{3} / G$ always…

math.DG2012★ 16 cited

$G_{2}$ -instantons, associative submanifolds, and Fueter sections

Thomas Walpuski

We give a sufficient condition for an associative submanifold in a G2-manifold to appear as the bubbling locus of a sequence of G2-instantons, related to the existence of a Fueter…

math.DG2011★ 27 cited

$G_{2}$ -instantons on generalised Kummer constructions

Thomas Walpuski

In this article we introduce a method to construct $G_{2}$ -instantons on $G_{2}$ -manifolds arising from Joyce's generalised Kummer construction. The method is based on gluing…

math.RA2010★ 27 cited

Notes on the octonions

Dietmar A. Salamon, Thomas Walpuski

This is an expository paper. Its purpose is to explain the linear algebra that underlies Donaldson-Thomas theory and the geometry of Riemannian manifolds with holonomy in $G_{2}$ and…

The universal moduli space of non-degenerate Z/2Z harmonic spinors

Dirac operators twisted by ramified Euclidean line bundles

Chambered invariants of real Cauchy-Riemann operators

Associative submanifolds in Joyce's generalised Kummer constructions

The Gopakumar-Vafa finiteness conjecture

Equivariant Brill-Noether theory for elliptic operators and super-rigidity of J-holomorphic maps

Counting embedded curves in symplectic 6-manifolds

On the compactness problem for a family of generalized Seiberg-Witten equations in dimension three

Hecke modifications of Higgs bundles and the extended Bogomolny equation

Castelnuovo's bound and rigidity in almost complex geometry

On counting associative submanifolds and Seiberg-Witten monopoles

On the existence of harmonic Z2​ spinors

Deformation theory of the blown-up Seiberg-Witten equation in dimension three

Tangent cones of Hermitian Yang-Mills connections with isolated singularities

Hermitian Yang-Mills metrics on reflexive sheaves over asymptotically cylindrical Kähler manifolds

A compactness theorem for Fueter sections

G2​-instantons over twisted connected sums: an example

Spin(7)-instantons, Cayley submanifolds, and Fueter sections

A compactness theorem for the Seiberg-Witten equation with multiple spinors in dimension three

G2​-instantons on twisted connected sums

Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three

G2​-instantons, associative submanifolds, and Fueter sections

G2​-instantons on generalised Kummer constructions

Notes on the octonions

The universal moduli space of non-degenerate $Z /2 Z$ harmonic spinors

Equivariant Brill-Noether theory for elliptic operators and super-rigidity of $J$ -holomorphic maps

On the existence of harmonic $Z_{2}$ spinors

$G_{2}$ -instantons over twisted connected sums: an example

$G_{2}$ -instantons on twisted connected sums

$G_{2}$ -instantons, associative submanifolds, and Fueter sections

$G_{2}$ -instantons on generalised Kummer constructions