Papers

Below is a list of the research, survey articles and lecture notes I have written. You can also find all of my research articles on the ArXiv.

Research articles

  1. Hypersymplecic strucures invariant under an effective circle action
    Joel Fine, Weiyong He, Chengjian Yao
    arxiv:2503.05272
  2. Seiberg-Witten equations in all dimensions.
    Joel Fine, Partha Ghosh
    arxiv:2411.09348
  3. Convergence of the hypersymplectic flow on T4 with T3-symmetry.
    Joel Fine, Weiyong He and Chengjian Yao
    To appear, Jour. London Math. Soc.
    arxiv:2404.15016
  4. Non-degeneracy of Poincaré-Einstein four-manifolds satisfying a chiral curvature inequality.
    Joel Fine.
    J. Geom. Anal. 33, article 249, 2023
    arxiv:2212.00526
  5. Knots, minimal surfaces and J-holomorphic curves.
    Joel Fine.
    arxiv:2112.07713
  6. A report on the hypersymplectic flow.
    Joel Fine, Chengjian Yao
    Pure Appl. Math. Q., Issue in honour of Simon Donaldson, 15:4, 1219-1260, 2019.
    arxiv:2001.11755
  7. Local rigidity of Einstein 4-manifolds satisfying a chiral curvature condition.
    Joel Fine, Kirill Krasnov, Michael Singer.
    Math. Ann. 379, pages 569-588, 2021.
    arxiv:1910.09790
  8. An ambient approach to conformal geodesics.
    Joel Fine, Yannick Herfray.
    Commun. Contemp. Math. 24:03 article number 2150009, 2022.
    arxiv:1907.02701
  9. Symplectic domination.
    Joel Fine, Dmitri Panov.
    Bull. London Math. Soc. doi:10.1112/blms.12402, 2020.
    arxiv:1905.05671
  10. Examples of compact Einstein four-manifolds with negative curvature.
    Joel Fine, Bruno Premoselli.
    J. Amer. Math. Soc 33, 991-1038, 2020
    arxiv:1802.00608
  11. Hypersymplectic 4-manifolds, the G2-Laplacian flow and extension assuming bounded scalar curvature.
    Joel Fine, Chengjian Yao.
    Duke Math. J. 167(18), 3533-3589, 2018
    arxiv:1704.07620
  12. The space of hyperkähler metrics on a 4-manifold with boundary.
    Joel Fine, Jason D. Lotay, Michael Singer.
    Forum of Mathematics, Sigma vol 5, 2017 50pp.
    arxiv:1603.08170
  13. Limits of Riemannian 4-manifolds and the symplectic geometry of their twistor spaces.
    Joel Fine.
    Transactions of the LMS 4(1), 100-109, 2017.
    arxiv:1602.03829
  14. Asymptotically hyperbolic connections.
    Joel Fine, Yannick Herfray, Kirill Krasnov, Carlos Scarinci.
    Class. Quantum Grav. 33 (2016), no 18, 25pp.
    arxiv:1512.07109
  15. Circle invariant fat bundles and symplectic Fano 6-manifolds.
    Joel Fine, Dmitri Panov.
    J. London Math. Soc. 91(3) 709-730, 2015.
    arxiv:1407.0840
  16. A gauge theoretic approach to Einstein 4-manifolds.
    Joel Fine, Kirill Krasnov, Dmitri Panov.
    New York J. Math. 20 293-323, 2014.
    arxiv:1312.2831
  17. A gauge theoretic approach to the anti-self-dual Einstein equations.
    Joel Fine.
    arxiv:1111.5005
  18. The diversity of symplectic Calabi-Yau six-manifolds.
    Joel Fine, Dmitri Panov.
    J. Toplogy, 6(1), 2013.
    arxiv:1108.5994
  19. The Hamiltonian geometry of the space of unitary connections with symplectic curvature.
    Joel Fine.
    J. Symplectic Geom. 12(1) 105-123, 2014.
    arxiv:1101.2420
  20. Quantisation and the Hessian of Mabuchi energy.
    Joel Fine.
    Duke Math. J. 161(14), 2753-2798, 2012.
    arxiv:1009.4543
  21. Hyperbolic geometry and non-Kähler manifolds with trivial canonical bundle.
    Joel Fine, Dmitri Panov.
    Geometry and Topology, 14, 1723-1763, 2010.
    arxiv:0905.3237
  22. Calabi flow and projective embeddings.
    Joel Fine.
    J. Differential Geom. 84(3), 489-523, 2010.
    arxiv:0811.0155
  23. Building symplectic manifolds using hyperbolic geometry.
    Joel Fine, Dmitri Panov.
    J. Gökova Geom. Top., 124-136, 2009.
    Preprint
  24. Symplectic Calabi-Yau manifolds, minimal surfaces and the hyperbolic geometry of the conifold.
    Joel Fine, Dmitri Panov.
    J. Differential Geom., 82(1), 155-205, 2009.
    arxiv:0802.3648
  25. Toric anti-self-dual Einstein metrics via complex geometry.
    Joel Fine.
    Math. Ann. 340(1), 143-157, 2008.
    arxiv:math/0609487
  26. A note on positivity of the CM line bundle.
    Joel Fine, Julius Ross.
    Int. Math. Res. Not., Article ID 95875, 14pp, 2006.
    arxiv:math/0605302
  27. Toric anti-self-dual 4-manifolds via complex geometry.
    Simon Donaldson, Joel Fine.
    Math. Ann., 336(2), 281-309, 2006.
    arxiv:math/0602423
  28. Fibrations with constant scalar curvature Kähler metrics and the CM-line bundle.
    Joel Fine.
    Math. Res. Lett., 14(2), 239-247, 2007.
    arxiv:math/0510075
  29. Constant scalar curvature Kähler metrics on fibred complex surfaces.
    Joel Fine.
    J. Differential Geom., 68(3), 397-432, 2004.
    arxiv:math/0401275
  30. Constant scalar curvature metrics on fibred complex surfaces.
    Joel Fine.
    PhD thesis, University of London, 2004.
    pdf ps

Survey articles and notes