Geometry

The faculty of the research group are active in the fields of Algebraic Geometry (Elena Guardo, Francesco Russo, Giovanni Staglianò, Giuseppe Zappalà) of General Topology (Angelo Bella) and in Combinatorics (Paola Bonacini, Mario Gionfriddo, Lucia Marino). The main research interests are:

Zero-Dimensional schemes and applications: we study  Hilbert functions and Betti numbers of zero-dimensional scehmes; in particular, we focus on low codimensional subschemes of  products of projective spaces  (E. Guardo, G. Zappalà).
Weak and Strong Lefschetz Properties for zero-dimensional rings: we mainly focus on zero-dimensional Gorenstein rings. The  vanishing of higher Hessians is closely related with the Weak (or Strong) Lefschetz property for standard graded Artinian Gorenstein algebras. In particular,  the vanishing higher hessians are  useful tools to get new interesting examples of  Artinian Gorenstein algebras which do not satisfy the Weak  (or Strong) Lefschetz property and/or new classification results (E. Guardo, F. Russo, G. Zappalà).
Geometry of projective varieties: we study embedded projective varieties with special geometric properties: secant defectiveness, dual defectiveness, Waring problem, star configurations, complete intersections and Hartshorne’s conjecture (E. Guardo, F. Russo, G. Staglianò)
Rationality of cubic hypersurfaces: rationality of special classes of smooth cubic hypersurfaces of P^5 (F. Russo, G. Staglianò).
Combinatorial Algebraic Geometry:  Combinatorics and Algebraic Geometry have classically enjoyed a fruitful interplay.  The topics involve classical algebraic varieties endowed with a rich combinatorial structure: toric varieties, matroids, polyhedral, multilinear algebra, hyperplane arrangements, determinantal varieties (E. Guardo).
General topology: It focuses on cardinal invariants for topological spaces, convergence properties and infinite topological games. The research often uses techniques from logic and set theory, like for example infinite combinatorics (A. Bella).
Design Theory, Graph and Hypergraphs Theory: In particular, we study decompositions of complete graphs K_n and complete r-uniform hypergraphs K^r_n, respectively in blocks of G-graphs and H-hypergraphs that are isomorphic between them. We study new classes of colorings where we focus on the importance of the upper chromatic number (other than the classic lower chromatic number) (P. Bonacini, M. Gionfriddo, E. Guardo, L. Marino).