Thomas Walpuski


  1. The Gopakumar–Vafa finiteness conjecture joint with Doan, A. and Ionel, E.
  2. Counting embedded curves in symplectic 6–manifolds joint with Doan, A.
  3. Arithmetic conditions for the existence of G2–instantons over twisted connected sums
  4. Equivariant Brill–Noether theory for elliptic operators and super-rigidity of J–holomorphic maps joint with Doan, A.


  1. On the existence of harmonic Z2 spinors joint with Doan, A. in Journal of Differential Geometry 117.3 (2021) pp. 395–449
  2. Castelnuovo’s bound and rigidity in almost complex geometry joint with Doan, A. in Advances in Mathematics 379 (2021)
  3. Deformation theory of the blown-up Seiberg–Witten equation in dimension three joint with Doan, A. in Selecta Mathematica 26.3 (2020)
  4. 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
  5. On counting associative submanifolds and Seiberg–Witten monopoles joint with Doan, A. in Pure and Applied Mathematics Quarterly 15.4 (2019) pp. 1047–1133
  6. On the compactness problem for a family of generalized Seiberg–Witten equations in dimension three joint with Zhang, B. to appear in Duke Mathematical Journal
  7. Hecke modifications of Higgs bundles and the extended Bogomolny equation joint with He, S. in Journal of Geometry and Physics 146 (2019)
  8. 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
  9. G2–instantons, associative submanifolds, and Fueter sections in Communications in Analysis and Geometry 25.4 (2017) pp. 847–893
  10. A compactness theorem for Fueter sections in Commentarii Mathematici Helvetici 92.4 (2017) pp. 751–776
  11. Notes on the octonions joint with Salamon, D. A. in Proceedings of the 23rd Gökova Geometry–Topology Conference (2017) pp. 1–85
  12. 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)
  13. Spin(7)–instantons, Cayley submanifolds, and Fueter sections in Communications in Mathematical Physics 352.1 (2016) pp. 1–36
  14. G2–instantons over twisted connected sums: an example in Mathematical Research Letters 23.2 (2016) pp. 529–544
  15. 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
  16. G2–instantons over twisted connected sums joint with Sá Earp, H. N. in Geometry and Topology 19.3 (2015) pp. 1263–1285
  17. G2–instantons on generalised Kummer constructions in Geometry and Topology 17.4 (2013) pp. 2345–2388