I am interested to complex (algebraic) geometry, in particular:

1. positivity conditions for vector and principal (Higgs) bundles;
2. moduli spaces of (principal) Higgs bundles;
3. complex projective varieties with Hessian indeterminated.

I am intrigued by:

1. cohomology of compact Kähler spaces (compact, complex, reduced analytic spaces with a Kähler form);
2. singularites of (Poincaré) normal functions;
3. counting curves and sheaves on K3 surfaces;
4. Hopf algebra cohomology;
5. curves on Abelian surfaces and on surfaces of general type.