On the cohomology of some exceptional symmetric spaces

This is a survey on the construction of a canonical or "octonionic K\"ahler" 8-form, representing one of the generators of the cohomology of the four Cayley-Rosenfeld projective planes. The construction, in terms of the associated even Clifford structures, draws a parallel with that of the quaternion K\"ahler 4-form. We point out how these notions allow to describe the primitive Betti numbers with respect to different even Clifford structures, on most of the exceptional symmetric spaces of compact type.Comment: 12 pages. Proc. INdAM Workshop "New Perspectives in Differential Geometry" held in Rome, Nov. 2015, to appear in Springer-INdAM Serie

On Schubert's Problem of Characteristics

The Schubert varieties on a flag manifold G/P give rise to a cell decomposition on G/P whose Kronecker duals, known as the Schubert classes on G/P, form an additive base of the integral cohomology of G/P. The Schubert's problem of characteristics asks to express a monomial in the Schubert classes as a linear combination in the Schubert basis. We present a unified formula expressing the characteristics of a flag manifold G/P as polynomials in the Cartan numbers of the group G. As application we develop a direct approach to our recent works on the Schubert presentation of the cohomology rings of flag manifolds G/P.Comment: 27page

(11)C-methylaminoisobutyric acid (MeAIB) PET for evaluation of prostate cancer: compared with (18)F-fluorodeoxyglucose PET.

α-N-methyl-(11)C-methylaminoisobutyric acid ((11)C-MeAIB) is a selective substrate of system A amino acid transport, and known to accumulate in malignant lesions. The aim of this study was to evaluate the utility of MeAIB PET for the assessment of prostate cancer, compared with FDG PET