Thomas Walpuski

D311 Wells Hall (PGP public key)


This Spring 2019, I am teaching MTH931: Riemannian Geometry, II. The course meets Tuesdays and Thursdays 12:40–2:00 PM in C517 Wells Hall. Here is a set of notes for this course (work in progress).

My office hours are Mondays 11am–12n and Fridays 2–3pm, or by appointment.



  1. On the compactness problem for a family of generalized Seiberg–Witten equations in dimension three
    with Boyu Zhang
  2. Hecke modifications of Higgs bundles and the extended Bogomolny equation
    with Siqi He
  3. Castelnuovo’s bound and rigidity in almost complex geometry
    with Aleksander Doan
  4. Equivariant Brill–Noether theory for elliptic operators and super-rigidity of J–holomorphic maps
    with Aleksander Doan
  5. On counting associative submanifolds and Seiberg–Witten monopoles
    with Aleksander Doan


  1. Deformation theory of the blown-up Seiberg–Witten equation in dimension three
    with Aleksander Doan
    accepted for publication in Selecta Mathematica
  2. On the existence of harmonic Z2 spinors
    with Aleksander Doan
    accepted for publication in Journal of Differential Geometry
  3. Hermitian Yang–Mills metrics on reflexive sheaves over asymptotically cylindrical Kähler manifolds
    with Adam Jacob
    Communications in Partial Differential Equations 43 11 1566—1598 2018
  4. Tangent cones of Hermitian Yang–Mills connections with isolated singularities
    with Adam Jacob and Henrique Sá Earp
    Mathematical Research Letters 25 5 1429–1445 2018
  5. G2–instantons, associative submanifolds, and Fueter sections
    Communication in Analysis and Geometry 25 4 847–893 2017
  6. A compactness theorem for Fueter sections
    Commentarii Mathematici Helvetici 92 4 751–776 2017
  7. Spin(7)–instantons, Cayley submanifolds, and Fueter sections
    Communications in Mathematical Physics 352 1 1–36 2017
  8. Notes on the octonions
    with Dietmar Salamon
    Proceedings of the 23rd Gökova Geometry–Topology Conference 1–85 2017
  9. G2–instantons over twisted connected sums: an example
    Mathematical Research Letters 23 2 529–544 2016
  10. Rigid HYM connections on tautological bundles over ALE crepant resolutions in dimension three
    with Anda Degeratu
    Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 12 17 2016
  11. A compactness theorem for the Seiberg–Witten equation with multiple spinors in dimension three
    with Andriy Haydys
    Geometric and Functional Analysis 25 5 1799–1821 2015
  12. G2–instantons over twisted connected sums
    with Henrique Sá Earp
    Geometry and Topology 19 3 1263–1285 2015
  13. G2–instantons over generalised Kummer constructions
    Geometry and Topology 17 5 2345–2388 2013

Lecture notes