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 (Alessio Corti)
September 18 2013
Existence of Minimal Models (Paolo Cascini)
On the classification of Fano lattice polygons under mutations (Alessio Corti)
September 19 2013
Existence of Mori Fiber spaces (Paolo Cascini)
Toric MMP and SOD (Yujiro Kawamata)
September 20 2013
Termination of flips (Paolo Cascini)
Individual meetings
September 23 2013
Minimal Model Program in positive characteristic (Paolo Cascini)
Some conjectures on the classification of orbifold del Pezzo surfaces (Alessio Corti)
Individual meetings
September 24 2013
Sarkisov Program (Paolo Cascini)
The Chen-Ruan cohomology of orbifolds (Alessio Corti)
Individual meetings
September 25 2013
Fedder criterion (Paolo Cascini)
The quantum cohomology of orbifolds (Alessio Corti)
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 (Paolo Cascini)
Smooth Delighe-Mumford toric stacks as geometric invariant theory quotients (Alessio Corti)
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 (Alessio Corti)
Individual meetings
October 3 2013
Presentations of the open problems by the participants
October 4 2013
Presentations of the open problems by the participants