Thomas Walpuski

Research

Preprints

  1. Arithmetic conditions for the existence of G2–instantons over twisted connected sums
  2. On the compactness problem for a family of generalized Seiberg–Witten equations in dimension three joint with Zhang, B.
  3. Castelnuovo’s bound and rigidity in almost complex geometry joint with Doan, A.
  4. Equivariant Brill–Noether theory for elliptic operators and super-rigidity of J–holomorphic maps joint with Doan, A.
  5. On counting associative submanifolds and Seiberg–Witten monopoles joint with Doan, A.

Publications

  1. 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
  2. Deformation theory of the blown-up Seiberg–Witten equation in dimension three joint with Doan, A. to appear in Selecta Mathematica
  3. Hecke modifications of Higgs bundles and the extended Bogomolny equation joint with He, S. to appear in Journal of Geometry and Physics
  4. On the existence of harmonic Z2 spinors joint with Doan, A. to appear in Journal of Differential Geometry
  5. 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
  6. A compactness theorem for Fueter sections in Commentarii Mathematici Helvetici 92.4 (2017) pp. 751–776
  7. G2–instantons, associative submanifolds, and Fueter sections in Communications in Analysis and Geometry 25.4 (2017) pp. 847–893
  8. Notes on the octonions joint with Salamon, D. A. in Proceedings of the 23rd Gökova Geometry–Topology Conference (2017) pp. 1–85
  9. Spin(7)–instantons, Cayley submanifolds, and Fueter sections in Communications in Mathematical Physics 352.1 (2016) pp. 1–36
  10. G2–instantons over twisted connected sums: an example in Mathematical Research Letters 23.2 (2016) pp. 529–544
  11. 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)
  12. G2–instantons over twisted connected sums joint with Sá Earp, H. N. in Geometry and Topology 19.3 (2015) pp. 1263–1285
  13. 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
  14. G2–instantons on generalised Kummer constructions in Geometry and Topology 17.4 (2013) pp. 2345–2388