Coherent sheaves and vector bundles on complex projective manifolds: study of simplicity and stability criteria, construction of moduli spaces and study of their properties, study of special vector bundles, like Steiner bundles, exceptional bundles, bundles without intermediate cohomology.
Higher secant varieties to complex projective varieties: defectivity of projective varieties, Terracini loci, postulation of zero-dimensional schemes. Waring’s problem.
Linear systems and interpolation problems in higher dimensional manifolds, specialities of linear systems, base locus, obstructions. Birational aspects: Mori dream spaces. Cones of divisors and curves and study of duality.
Tensors and applications of algebraic geometry. Complex and real rank. Identifiability.
