Research topics

The projects to be discussed at this workshop can be grouped broadly into two (related) areas, which we briefly describe below.

Fano manifolds and Mirror Symmetry (Alessio Corti)

The motivating philosophy of this new field is that Fano manifolds can be classified by classifying their Laurent polynomial mirrors. More precisely: starting from a Laurent polynomial f, one may construct a Picard–Fuchs differential operator Lf. Similarly, a Fano manifold X determines an associated regularised quantum differential operator QX, which encodes its quantum cohomology. A Laurent polynomial f is said to be mirror-dual to the Fano manifold X if Lf = QX. Recent work of Corti, Coates et al. reconstructs the classification of smooth del Pezzo surfaces and the Iskovskikh-Mori-Mukai classification of smooth Fano 3-folds by studying Laurent polynomials supported on reflexive polytopes. The projects which fall in this area are studying the possibility of extending the methods of Corti, Coates et al. to singular del Pezzo surfaces (equivalently: Fano orbifold surfaces).

On the Minimal Model Program (Paolo Cascini)

The aim of the minimal model program is to generalize the classification of complex projective surfaces, known in the early 20th century, to higher dimensional varieties. The projects which fall in this area involve applications and new aspects of this programme.

The abstracts of the talks are available at Schedule.