"Atomic and twisted sheaves on varieties with trivial canonical bundle"

Abstract:

The two courses aim at presenting two apparently different but intimately related theories about sheaves on manifolds: the one about atomic sheaves and the one about twisted ones.

The first course will present some recent advances in the theory of stable sheaves on higher dimensional hyper-Kähler manifolds. First we will review Mukai's theory on K3 surfaces. Then we will consider hyper-Kähler fourfolds and this will naturally lead us to introduce
the recent theory of atomic sheaves. In this direction, we will discuss general results due to O'Grady, Markman, Beckmann, and Bottini.

The second course will be about twisted sheaves and their many appearances in algebraic geometry. After surveying some foundational material about Brauer groups and twisted sheaves, we will focus on the construction of moduli spaces of twisted sheaves and their relation with Hodge theory. In this direction we will review the proof of Shafarevich conjecture and the role of twisted sheaves in the recent proofs of some cases of the Hodge conjecture. On the more arithmetic side we will discuss some recent striking results proving the so-called period-index conjecture for Brauer groups which encodes a deep relationship between two natural invariants associated to elements of the Brauer group.

One of the objectives of the two courses is to show the fruitful interplay between the two subjects.

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: pragmatic@dmi.unict.it

The deadline for  applications is April 30th, 2025. The Committee of Pragmatic will decide about financial supports and admissions within May 15th, 2025.
Interested people who need more information about Pragmatic can contact any member of the local committee.

The Organization of Pragmatic 2025 will cover the boarding and lodging expenses (double room B&B accomodation) of the participants which are not supported by their institutions, but not the travel expenses.

      ___________________________________________________________________

APPLICATION FORM TO PRAGMATIC 2025

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:

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

_______________________________________________________________________________________________

Scientific Committee:

Alex Massarenti - Università di Ferrara

Francesco Russo - Università di Catania

Organizers:

Elena Guardo  - Università di Catania

Francesco Russo  - Università di Catania

Giovanni Staglianò - Università di Catania

Giuseppe Zappalà - Università di Catania

Alfio Ragusa  - Università di Catania