SCHOOL (AND WORKSHOP) ON

HODGE THEORY AND ALGEBRAIC GEOMETRY

TRENTO, AUGUST 31-SEPTEMBER 5, 2009




First announcement


Lecturers.

E. Looijenga (Universiteit Utrecht, Nl)
C. Voisin (CNRS and IHES – Fr)

Organizers.
The School/Workshop is organized by G. Casnati, A.J. Di Scala, R. Notari, S. Salamon. For contacting the organizers send a mail to

geometri [nospam] calvino.polito.it

Aim of the School.
The School is mainly aimed to Phd students and young researchers in Algebraic Geometry, introducing the participants to research, beginning from a basic level with a view towards the applications and to the most recent results.
From the historical and scientific viewpoint, Hodge theory as developed by Griffiths and Deligne since the 70's is a powerful tool for studying algebraic varieties in characteristic zero. It consists mostly in the study of the (mixed) Hodge structures associated to algebraic varieties, and their variations. The so-called period map allows one to study moduli spaces qualitatively and the natural local systems of cohomology on them. Sometimes it even gives a uniformization of the relevant moduli spaces. Another aspect of Hodge theory is the study of the Hodge conjecture and its variants (generalized Hodge conjecture, variational Hodge conjecture). These two aspects are related via the study of Hodge loci, which are natural subloci of moduli spaces.
The whole subject presents a mixture of topology, complex geometry, Lie group theory and of course algebraic geometry, which is rather fascinating. The best example of this is the fact that the constant local systems underlying variations of Hodge structures are of a topological nature, while the variation of Hodge structure itself and the Hodge bundles can be defined inside algebraic geometry. Hodge theory is increasingly used in the context of Differential Geometry for the calculation of Dolbeault cohomology of manifolds with special structures generalizing Kähler geometry.

Further announcements.
A more detailed second announcement (containing informations on accomodation, registration and financial supports) will follow probably in February 2009.