Scientific activities

All
the topics and the open problems were related to “Higher
Dimensional Algebraic Geometry".
During the courses the teachers introduced all basic facts on the
Minimal Model Program to generalize the classification of complex
projective surfaces to higher dimensional. Moreover, using the
Laurent polynomial f, they constructed the Picard--Fuchs differential
operator L_f. Certain facts about the quantum cohomology of a Fano
manifold X, introduced the regularised quantum differential operator
Q_X. During the period were addressed more than 10 open problems
which were attached by the participants divided in several groups.

Here is the schedule of the seminars and individual meetings during the period of the school.

Introduction to the Minimal Model Program

Minimal Model Program with scaling

Existence of Minimal Models

Existence of Mori Fiber spaces

Termination of flips

Fedder's criterion

Minimal Model Program in positive characteristic

Sarkisov Program

Shokurov's Log Geography

Boundedness in birational geometry

**Calendars
of seminars**

**September 16 2013**

*Introduction to the Minimal Model Program*(Paolo Cascini)*The Fano/Landau Ginzburg correspondence*(Alessio Corti)

**September 17 2013**

*Minimal Model Program with scaling*(Paolo Cascini)*Laurent polynomials and their classical periods*

**September 18 2013**

*Existence of Minimal Models*(Paolo Cascini)*On the classification of Fano lattice polygons under mutations*

**September 19 2013**

*Existence of Mori Fiber spaces*(Paolo Cascini)*Toric MMP and SOD*

**September 20 2013**

*Termination of flips*(Paolo Cascini)

Individual meetings

**September 23****
2013**

*Mi**nimal Model Program in positive characteristic*(Paolo Cascini)*Some conjectures on the classification of orbifold del Pezzo surfaces*

Individual meetings

**September 24 2013***
*

*S**arkisov Program*(Paolo Cascini)*The Chen-Ruan cohomology of orbifolds*

Individual meetings

**September
25 2013**

*Fedder criterion**The quantum cohomology of orbifolds*

Individual meetings

**September 26****
2013**

*Shokurov’s Log Geography*(Paolo Cascini)*Derived categories of weighted projective space*(Yujiro Kawamata)

**September 27 2013***
*

*Boundededness in birational geometry**Smooth Delighe-Mumford toric stacks as geometric invariant theory quotients*

Individual meetings

**September
30 2013**

*The quantum orbifold cohomology of smooth Deligne-Mumford Fano toric stacks*

(Alessio Corti)

Individual meetings

**October
1 2013**

*The quantum Lefschetz theorem for stacks*(Alessio Corti)

Individual meetings

**October
2 2013**

*The monodromy at infinity of hypersurfaces in tori*

Individual meetings

**October
3 2013**

Presentations of the open problems by the participants

**October
4 2013**

Presentations of the open problems by the participants