Research
Preprints

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

On the compactness problem for a family of generalized Seiberg–Witten equations in dimension three
joint with Zhang, B.

Castelnuovo’s bound and rigidity in almost complex geometry
joint with Doan, A.

Equivariant Brill–Noether theory for elliptic operators and superrigidity of J–holomorphic maps
joint with Doan, A.

On counting associative submanifolds and Seiberg–Witten monopoles
joint with Doan, A.
Publications

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

Deformation theory of the blownup Seiberg–Witten equation in dimension three
joint with Doan, A.
to appear in Selecta Mathematica

Hecke modifications of Higgs bundles and the extended Bogomolny equation
joint with He, S.
to appear in Journal of Geometry and Physics

On the existence of harmonic Z_{2} spinors
joint with Doan, A.
to appear in Journal of Differential Geometry

Tangent cones of Hermitian Yang–Mills connections with isolated singularities
joint with Jacob, A. and Sá Earp, H. 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

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

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

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

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

G_{2}–instantons over twisted connected sums
joint with Sá Earp, H. 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, A.
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