Peter Dalakov


My main interests are in non-abelian Hodge theory, opers and geometry of moduli of Higgs bundles. I am also interested in various deformation-theoretic techniques that arise in this context.

The following is a mixture of: 1) Topics that I actively think about 2) Broad interests 3) Ever-expanding wish list:

  • · Moduli of Higgs bundles, the Hitchin system. NAHT and opers.
  • · Special Kähler geometry, mostly on the Hitchin base.

  • · Deformation theory, DGLA's and L-infinity algebras; derived AG
  • · The interplay between NAHT, mirror symmetry, geometric Langlands and S-duality

  • · Holomorphic Poisson geometry and its relation to non-commutative geometry
  • · Generalised Kähler geometry and non-commutative instantons
  • · Springer theory
  • · Special geometries, Hermitian geometry.

    Papers and preprints:

  • · Lectures on Higgs moduli and abelianisation, J. Geom. Phys., vol. 118, 2017, pp.94--125, also arXiv.AG 1609.00646
  • · Meromorphic Higgs bundles and related geometries, J. Geom. Phys., vol. 109, 2016, pp. 44-67, also arXiv.AG 1602.03672
  • · Donagi-Markman cubic for the generalised Hitchin system, with Ugo Bruzzo, Int. J. Math., vol. 25 (2), 2014, also arXiv.AG 1308.6788
  • · On the L-infinity description of the Hitchin map, Rend. Ist. Mat. Univ. Trieste, vol.46 (2014), p.1-17, also arXiv.AG 1007.5309.
  • · arXiv.AG 1111.6457 I described holomorphic Darboux coordinates in a neighbourhood of the uniformising G-Higgs bundle
  • · Harmonic spinors of the Dirac operator of connection with torsion in dimension four with Stefan Ivanov, Class. Quant. Grav., vol. 18 (2), 2001


  • · PhD thesis: Higgs bundles and Opers at UPenn with Tony Pantev
  • · MS thesis: Eigenvalue estimates for Dirac operators of connections with Torsion with Stefan Ivanov


    " ...and signs and the signs of signs are used only when we are lacking things ", William of Baskerville