**SCHOOL (AND WORKSHOP) ON
**

**
**TRENTO, SEPTEMBER 12-17,
2011

**
**First announcement

**Lecturers.
**

S. Di Rocco(KTH Stockholm – Se)

G. Mikhalkin(Université de Genève – CH)

**Organizers.
**The School/Workshop is organized by G. Casnati, C. Fontanari, F.
Galluzzi, R. Notari, F. Vaccarino. For contacting the organizers send a
mail
to

**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.

S. Di Rocco. Toric
Geometry.

Toric varieties have provided a remarkably fertile testing ground for
general theories in Algebraic Geometry. The action of the algebraic
torus gives a rich combinatorial structure which not only
serves as a useful computational tool, but, equally importantly, as a
bridge to neighboring areas such as Combinatorics, Statistics, Biology
and more. The emphasis of this series of lectures is on the study of
the geometry of projective toric varieties and its relation to
convex geometry. In the first lecture normal projective toric varieties
and the correspondence with lattice convex polytopes will be
introduced. Basic notions and basic examples will be presented. The
remaining lectures will each introduce research areas in toric geometry
where problems are still open, typically in the singular case.

G. Mikhalkin. Tropical
Geometry.

The lectures will cover basic notions of tropical geometry with a focus
on their topological treatment. Tentatively the following topics will
be treated. Real 1-parametric families of complex manifolds and their
tropical limits. Matroids, integer affine structure, formal definition
of tropical variety. Projective spaces. Hypersurfaces and complete
intersections. Chow group vs. homological cycles in tropical varieties.
Intersection theory. Tropical waves and detecting algebraic cycles.
Moduli spaces of curves in tropical manifolds. Enumerative problems.
Reality questions. Connection to Mirror Symmetry and further topics.

**Further announcements.**

A more detailed second announcement (containing informations on
accomodation, registration and financial supports) will follow
probably in February 2011.