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

1. positivity conditions for vector and principal (Higgs) bundles;

2. curves on minimal surfaces of general type;

3. Hilbert vectors of Artinian graded algebras; 

4. moduli spaces of (principal) Higgs bundles.

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. Hopf algebra cohomology;

4. complex projective varieties with Hessian indeterminated.