Interests:
My main interests are in nonabelian Hodge theory, opers and geometry of moduli of Higgs bundles.
I am also interested in various deformationtheoretic techniques
that arise in this context.
The following is a mixture of: 1) Topics that I actively think about 2) Broad interests 3) Everexpanding 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 Linfinity algebras; derived AG
· The interplay between NAHT, mirror symmetry, geometric Langlands and Sduality
· Holomorphic Poisson geometry and its relation to noncommutative geometry
· Generalised Kähler geometry and noncommutative instantons
· Springer theory
· Special geometries, Hermitian geometry.
Papers and preprints:
· Lectures on Higgs moduli and abelianisation,
J. Geom. Phys., vol. 118, 2017, pp.94125,
also
arXiv.AG 1609.00646
· Meromorphic Higgs bundles and related geometries, J. Geom. Phys., vol. 109, 2016,
pp. 4467,
also arXiv.AG 1602.03672
·
DonagiMarkman cubic for the generalised Hitchin system, with
Ugo Bruzzo, Int. J. Math., vol. 25 (2), 2014, also
arXiv.AG 1308.6788
· On the Linfinity description of the Hitchin map,
Rend. Ist. Mat. Univ. Trieste, vol.46 (2014), p.117, also arXiv.AG 1007.5309.
· arXiv.AG 1111.6457 I described holomorphic Darboux coordinates in a neighbourhood of the uniformising
GHiggs bundle
· Harmonic spinors of the Dirac operator of connection with torsion in dimension four with Stefan Ivanov,
Class. Quant. Grav., vol. 18 (2), 2001
Theses:
· 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
CV
