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. 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.
  2. Local rigidity of Einstein 4-manifolds satisfying a chiral curvature condition.
    Joel Fine, Kirill Krasnov, Michael Singer.
    To appear in Math. Ann.
  3. An ambient approach to conformal geodesics.
    Joel Fine, Yannick Herfray.
  4. Symplectic domination.
    Joel Fine, Dmitri Panov.
    Bull. London. Math. Soc. doi:10.1112/blms.12402, 2020.
  5. Examples of compact Einstein four-manifolds with negative curvature.
    Joel Fine, Bruno Premoselli.
    J. Amer. Math. Soc 33, 991-1038, 2020
  6. 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
  7. 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.
  8. Limits of Riemannian 4-manifolds and the symplectic geometry of their twistor spaces.
    Joel Fine.
    Transactions of the LMS 4(1), 100-109, 2017.
  9. Asymptotically hyperbolic connections.
    Joel Fine, Yannick Herfray, Kirill Krasnov, Carlos Scarinci.
    Class. Quantum Grav. 33 (2016), no 18, 25pp.
  10. Circle invariant fat bundles and symplectic Fano 6-manifolds.
    Joel Fine, Dmitri Panov.
    J. London Math. Soc. 91(3) 709-730, 2015.
  11. A gauge theoretic approach to Einstein 4-manifolds.
    Joel Fine, Kirill Krasnov, Dmitri Panov.
    New York J. Math. 20 293-323, 2014.
  12. A gauge theoretic approach to the anti-self-dual Einstein equations.
    Joel Fine.
  13. The diversity of symplectic Calabi-Yau six-manifolds.
    Joel Fine, Dmitri Panov.
    J. Toplogy, 6(1), 2013.
  14. The Hamiltonian geometry of the space of unitary connections with symplectic curvature.
    Joel Fine.
    J. Symplectic Geom. 12(1) 105-123, 2014.
  15. Quantisation and the Hessian of Mabuchi energy.
    Joel Fine.
    Duke Math. J. 161(14), 2753-2798, 2012.
  16. Hyperbolic geometry and non-Kähler manifolds with trivial canonical bundle.
    Joel Fine, Dmitri Panov.
    Geometry and Topology, 14, 1723-1763, 2010.
  17. Calabi flow and projective embeddings.
    Joel Fine.
    J. Differential Geom. 84(3), 489-523, 2010.
  18. Building symplectic manifolds using hyperbolic geometry.
    Joel Fine, Dmitri Panov.
    J. Gökova Geom. Top., 124-136, 2009.
  19. 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.
  20. Toric anti-self-dual Einstein metrics via complex geometry.
    Joel Fine.
    Math. Ann. 340(1), 143-157, 2008.
  21. A note on positivity of the CM line bundle.
    Joel Fine, Julius Ross.
    Int. Math. Res. Not., Article ID 95875, 14pp, 2006.
  22. Toric anti-self-dual 4-manifolds via complex geometry.
    Simon Donaldson, Joel Fine.
    Math. Ann., 336(2), 281-309, 2006.
  23. Fibrations with constant scalar curvature Kähler metrics and the CM-line bundle.
    Joel Fine.
    Math. Res. Lett., 14(2), 239-247, 2007.
  24. Constant scalar curvature Kähler metrics on fibred complex surfaces.
    Joel Fine.
    J. Differential Geom., 68(3), 397-432, 2004.
  25. Constant scalar curvature metrics on fibred complex surfaces.
    Joel Fine.
    PhD thesis, University of London, 2004.
    pdf ps

Survey articles and notes