SCHOOL (AND WORKSHOP) ON

TROPICAL AND TORIC GEOMETRY



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

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.
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.