Simone Diverio (SAPIENZA Università di Roma)

Title: Pointwise universal Gysin formulae and positivity of some characteristic forms

Abstract: 
In the last few years there has been a renewed interest around an old conjecture by Griffiths 
characterizing which should be the positive characteristic forms for any given Griffiths positive 
holomorphic Hermitian vector bundle. According to this conjecture, they should be precisely the 
characteristic forms belonging to the positive cone spanned by the Schur forms. After recalling 
the various notions of positivity for holomorphic Hermitian vector bundles, and how they are 
(or should be) related, we shall explain a recent result obtained in collaboration with my 
PhD student F. Fagioli, which gives a partial confirmation of the above conjecture. Such a result 
is obtained as a consequence of a pointwise, differential-geometric Gysin formula for the push-forward 
of the curvature of the tautological line bundles over flag bundles.