Preprints

The Gopakumar–Vafa finiteness conjecture
joint with
Doan, Aleksander
and
Ionel, ElenyN.

Arithmetic conditions for the existence of G_{2}–instantons over twisted connected sums
Publications

Associative submanifolds in Joyce’s generalised Kummer constructions
joint with
Dwivedi, Shubham
and
Platt, Daniel
in
Communications in Mathematical Physics
(2023)

Equivariant Brill–Noether theory for elliptic operators and superrigidity of J–holomorphic maps
joint with
Doan, Aleksander
in
Forum of Mathematics Sigma
11
(2023)

Counting embedded curves in symplectic 6–manifolds
joint with
Doan, Aleksander
to appear in Commentarii Mathematici Helvetici

On the compactness problem for a family of generalized Seiberg–Witten equations in dimension 3
joint with
Zhang, Boyu
in
Duke Mathematical Journal
170.17
(2021)
pp. 3891–3934

On the existence of harmonic Z_{2} spinors
joint with
Doan, Aleksander
in
Journal of Differential Geometry
117.3
(2021)
pp. 395–449

Castelnuovo’s bound and rigidity in almost complex geometry
joint with
Doan, Aleksander
in
Advances in Mathematics
379
(2021)

Deformation theory of the blownup Seiberg–Witten equation in dimension three
joint with
Doan, Aleksander
in
Selecta Mathematica
26.3
(2020)

On counting associative submanifolds and Seiberg–Witten monopoles
joint with
Doan, Aleksander
in
Pure and Applied Mathematics Quarterly
15.4
(2019)
pp. 1047–1133

Hecke modifications of Higgs bundles and the extended Bogomolny equation
joint with
He, Siqi
in
Journal of Geometry and Physics
146
(2019)

Hermitian Yang–Mills metrics on reflexive sheaves over asymptotically cylindrical Kähler manifolds
joint with
Jacob, A.
in
Communications in Partial Differential Equations
43.11
(2019)
pp. 1566–1598

Tangent cones of Hermitian Yang–Mills connections with isolated singularities
joint with
Jacob, Adam
and
Sá Earp, Henrique N.
in
Mathematical Research Letters
25.5
(2018)
pp. 1429–1445

A compactness theorem for Fueter sections
in
Commentarii Mathematici Helvetici
92.4
(2017)
pp. 751–776

Notes on the octonions
joint with
Salamon, Dietmar A.
in
Proceedings of the 23rd Gökova Geometry–Topology Conference
(2017)
pp. 1–85

G_{2}–instantons, associative submanifolds, and Fueter sections
in
Communications in Analysis and Geometry
25.4
(2017)
pp. 847–893

Rigid HYM connections on tautological bundles over ALE crepant resolutions in dimension three
joint with
Degeratu, Anda
in
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
12.17
(2016)

Spin(7)–instantons, Cayley submanifolds, and Fueter sections
in
Communications in Mathematical Physics
352.1
(2016)
pp. 1–36

G_{2}–instantons over twisted connected sums: an example
in
Mathematical Research Letters
23.2
(2016)
pp. 529–544

G_{2}–instantons over twisted connected sums
joint with
Sá Earp, Henrique N.
in
Geometry and Topology
19.3
(2015)
pp. 1263–1285

A compactness theorem for the Seiberg–Witten equation with multiple spinors in dimension three
joint with
Haydys, Andriy
in
Geometric and Functional Analysis
25.6
(2015)
pp. 1799–1821

G_{2}–instantons on generalised Kummer constructions
in
Geometry and Topology
17.4
(2013)
pp. 2345–2388
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