I am interested to complex (algebraic) geometry, in particular:
positivity conditions for vector and principal (Higgs) bundles;
moduli spaces of (principal) Higgs bundles;
Hilbert vector of standard graded Artinian Gorenstein algebras, and applications.
I am intrigued by:
cohomology of compact Kähler spaces (compact, complex, reduced analytic spaces with a Kähler form);
singularites of (Poincaré) normal functions;
Hopf algebra cohomology;
complex projective varieties with Hessian indeterminated;
curves on minimal surfaces of general type.