P.R.A.G.MAT.I.C.
2007
at University of Catania
(Promotion
of Research
in Algebraic
Geometry
for MAThematicians
in Isolated
Centres)
Second announcement
PRAGMATIC is a project, sponsored by INDAM, 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 and
will
give lectures and seminars and will have 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 that the participants obtain could be reproduced
in a special issue of the journal Le
Matematiche.
In the period July 9 - July
28, 2007,
at Dipartimento
di
Matematica e Informatica of the University
of
Catania, a
new edition of this
school of research Pragmatic 2007 will be held.
Teachers:
| Prof. Giuseppe Pareschi |
Università di Roma II
Tor Vergata |
| Prof. Mihnea Popa |
University
of Chicago |
| Collaborator: dott. Antonio Rapagnetta |
University of Liverpool |
Theme
of research: Fourier-Mukai
transforms, generic vanishing, and regularity
Scientific
activity.
The
aim of the course will be to provide an introduction to the use of
Fourier-Mukai transforms in the study of irregular varieties and moduli
spaces from a higher dimensional geometry point of view, and also to
their use in specific geometric problems related to abelian varieties,
for example the study of their defining equations, or detecting
Jacobians. The lectures and research problems will roughly focus on the
following subjects:
- Generalities
on derived categories, Base-Change, and Fourier-Mukai functors.
- Generalities on multiplier
ideals.
- Sheaves satisfying Generic
Vanishing and the Weak Index Theorem with respect to an arbitrary
Fourier-Mukai functor.
- Generic
vanishing theorems for irregular varieties and their relationship with
standard vanishing theorems like Kawamata-Viehweg and its extensions.
- Generic vanishing index and the
Fourier-Mukai transform as a k-th syzygy sheaf.
- M-regularity,
generation of sheaves, and applications to abelian varieties.
- Approaches to the geometric
Schottky problem based on regularity and generic vanishing.
A number of research problems will be
proposed to the participants at this school, according to their
respective backgrounds. Some might fall outside of the topics listed
above. As general prerequisites, we recommend familiarity with
basic algebraic geometry, with abelian varieties and with basic
homological
methods leading to the Serre-Grothendieck-Verdier duality theorem.
Scientific program with
references.
Pragmatic will accept about 15-20 young
participants and will support all the participants which are not able
to find support in their institutions.
This financial support
will be
awarded, essentially, to young researchers, say at the pre-postdoctoral
level, with preference given to those belonging to geographically
isolated locations. The support will cover lodging, boarding along all
period of Pragmatic, the cost of the fee and some travel expenses.
The Co-ordinator of Pragmatic is Prof. Alfio Ragusa
(University
of Catania). Other local organizers
are: Rosario Strano, Renato Maggioni, Salvatore Giuffrida, Giuseppe
Zappalà.
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 the
following address:
E-mail: zappalag@dmi.unict.it
| or
by ordinary mail to: |
Dott.
Giuseppe Zappalà, |
|
Dipartimento
di Matematica e Informatica, |
|
Viale
A. Doria 6, 95125 Catania - Italy.
|
or
E-mail: ragusa@dmi.unict.it
| or
by ordinary mail to: |
Prof.
Alfio Ragusa, |
|
Dipartimento
di Matematica e Informatica, |
|
Viale
A. Doria 6, 95125 Catania - Italy. |
The deadline for applications
is May 20th, 2007.
The Committee of Pragmatic will
decide about financial supports and admissions within May 2007 and will inform all the
applicants of the
outcome. Moreover
a
list of participants and
all the activities of the school will be spread by EAGER net. Interested people who need more
information about Pragmatic can contact any member of the
local
committee, using the following E-mail addresses: sstrano, maggioni, giuffrida,
zappalag (one of these)@dmi.unict.it
APPLICATION
FORM
TO PRAGMATIC 2007
Surname:
Name:
Male
or Female:
Date
of Birth:
Nationality:
Institution:
Academic
qualification
(Ph.D.,
Master,...):
Name
of advisor:
Professional
Status and Current
Position:
E-mail address:
Field
of interest:
Estimate
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
