|Research school in
Algebraic Geometry and Commutative Algebra
Sponsored by PRIN 2010-2011, PRA UNICT, INDAM (GNSAGA)
|Topics in Higher
Dimensional Algebraic Geometry
September 16th - October 4th, 2013
Lecturers: Prof. Alessio Corti, Prof. Paolo Cascini
with special lectures by Prof. Yujiro Kawamata
|Pragmatic Home Page
First announcement <<
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PRAGMATIC is a project, sponsored by PRIN 2010-2011, PRA UNICT, INDAM (GNSAGA), for stimulating research in Algebraic Geometry among young people, especially those living in isolated centres or peripheral universities all over Europe.
For this purpose, every year, a group of experts will suggest problems in some specific field through lectures, seminars and individual discussions with the participants in order to try to attack and to solve these problems.
At the end of all the activities of Pragmatic the results obtained by the participants could be submitted for publication in a special issue of the journal Le Matematiche.
In the period September 16th - October 4th, 2013, at Dipartimento di Matematica e Informatica of the University of Catania (Italy), a new edition of the school of research Pragmatic will be held.
During the first two weeks there will be also some special lectures by Prof. Yujiro Kawamata (University of Tokyo).
Theme of research: Topics in Higher Dimensional Algebraic Geometry
Fano manifolds and Mirror Symmetry (Prof. A. Corti)
Starting from a Laurent polynomial f, we explain how to construct the Picard--Fuchs differential operator L_f. Next we summarise certain facts about the quantum cohomology of a Fano manifold X, introducing the regularised quantum differential operator Q_X. A Laurent polynomial f is said to be mirror-dual to the Fano manifold X if L_f=Q_X. I demonstrate how to derive the classification of Fano 3-folds (Iskovskikh, Mori--Mukai) from the classification of their mirrors. We introduce a more sophisticated approach where the mirror is a global function on a cluster variety. We outline a program to classify Fano 4-folds using these ideas. This is a new subject with many accessible open problems, particularly if you are willing to work with computer algebra.
On the Minimal Model Program (Prof. P. Cascini)
The aim of the Minimal Model Program is to generalize the classification of complex projective surfaces, known in the early 20th century, to higher dimensional varieties. Besides providing a historical introduction, we will discuss some recent results, applications and new aspects of this Program.
Pragmatic will accept about 15-20 young participants and will cover the living expenses of all the participants who are not able to find support in their own institution.
The financial support will be given preferably to young researchers, say at the pre-postdoctoral level, and to those belonging to geographically isolated locations. The support will cover lodging and boarding and exceptionally a contribution for travel expenses.
The Co-ordinators of Pragmatic 2013 are Alfio Ragusa, Francesco Russo, Giuseppe Zappalą (University of Catania).
People who wish to be considered either for participation and/or for financial support should fill out the enclosed application form, which should be sent to one of the following address:
The deadline for applications is May 31th, 2013. The Committee of Pragmatic will decide about financial supports and admissions within June 10th, 2013. Interested people who need more information about Pragmatic can contact any member of the local committee.
APPLICATION FORM TO PRAGMATIC 2013
Male or Female:
Date of Birth:
Academic qualification (Ph.D., Master,...):
Name of advisor:
Professional Status and Current Position:
Field of interest:
Estimated cost of travel to Catania:
Can you be supported by your institution?: (Possible answers: totally, partly, no)
If you have a Ph.D, when did you get it and where?
Reasons for wanting to participate in the session:
It is suggested that the applications include both a recommendation letter and a brief Curriculum vitae