Preprints

1. The Gopakumar–Vafa finiteness conjecture joint with Doan, Aleksander and Ionel, Eleny-N.
2. Arithmetic conditions for the existence of G₂–instantons over twisted connected sums

Publications

1. Associative submanifolds in Joyce’s generalised Kummer constructions joint with Dwivedi, Shubham and Platt, Daniel in Communications in Mathematical Physics (2023)
2. Equivariant Brill–Noether theory for elliptic operators and super-rigidity of J–holomorphic maps joint with Doan, Aleksander in Forum of Mathematics Sigma 11 (2023)
3. Counting embedded curves in symplectic 6–manifolds joint with Doan, Aleksander to appear in Commentarii Mathematici Helvetici
4. 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
5. On the existence of harmonic Z₂ spinors joint with Doan, Aleksander in Journal of Differential Geometry 117.3 (2021) pp. 395–449
6. Castelnuovo’s bound and rigidity in almost complex geometry joint with Doan, Aleksander in Advances in Mathematics 379 (2021)
7. Deformation theory of the blown-up Seiberg–Witten equation in dimension three joint with Doan, Aleksander in Selecta Mathematica 26.3 (2020)
8. On counting associative submanifolds and Seiberg–Witten monopoles joint with Doan, Aleksander in Pure and Applied Mathematics Quarterly 15.4 (2019) pp. 1047–1133
9. Hecke modifications of Higgs bundles and the extended Bogomolny equation joint with He, Siqi in Journal of Geometry and Physics 146 (2019)
10. 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
11. 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
12. A compactness theorem for Fueter sections in Commentarii Mathematici Helvetici 92.4 (2017) pp. 751–776
13. Notes on the octonions joint with Salamon, Dietmar A. in Proceedings of the 23rd Gökova Geometry–Topology Conference (2017) pp. 1–85
14. G₂–instantons, associative submanifolds, and Fueter sections in Communications in Analysis and Geometry 25.4 (2017) pp. 847–893
15. 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)
16. Spin(7)–instantons, Cayley submanifolds, and Fueter sections in Communications in Mathematical Physics 352.1 (2016) pp. 1–36
17. G₂–instantons over twisted connected sums: an example in Mathematical Research Letters 23.2 (2016) pp. 529–544
18. G₂–instantons over twisted connected sums joint with Sá Earp, Henrique N. in Geometry and Topology 19.3 (2015) pp. 1263–1285
19. 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
20. G₂–instantons on generalised Kummer constructions in Geometry and Topology 17.4 (2013) pp. 2345–2388