Geometry and Algebra

a) Design theory, graph decompositions and their symmetries. The research activity focuses on Design Theory and Graph Decompositions with potential applications to the design of statistical experiments, and in areas such as Coding Theory, Communications Systems and Software Testing. One of the primary objectives is constructing designs which have desirable properties with respect to concepts such as symmetries, colorings, resolutions, and studying generalizations such as packing and covering designs. b) Incidence Geometry and polar spaces. This research activity is concerned with the study of Grassmannians of polar spaces and, more in general, incidence geometries in determining the possible ranks and dimensions and in describing their structure. This has applications both to the theory of Lie groups and to the study and construction on novel error correcting codes. c) Clifford parallelisms. The research is aimed at studying parallelisms in 3-dimensional projective spaces. In particular the target of the investigation are the Clifford parallelism arising in projective spaces associated to quaternion algebras. We focus on the study of Clifford-like parallelism, namely parallelisms whose parallel classes are either left or right Clifford parallel classes, and of their groups of automorphisms.