Organizers:
Alfio Ragusa  - Università di Catania
Elena Guardo  - Università di Catania
Francesco Russo  - Università di Catania
Giuseppe Zappalà - Università di Catania 

Lecturers:
Brian Harbourne - University of Nebraska, Lincoln, Nebraska (USA)
Adam Van Tuyl - McMaster University, Hamilton, Ontario (Canada)

Collaborators:
Enrico Carlini - Politecnico di Torino (Italy)
Tai Huy Ha - Tulane University New Orleans (USA)

Topic: Powers of ideals and ideals of powers

The topics are motivated by algebraic problems related to the relationship between various notions of powers of ideals, and by geometric problems related to secant varieties, including, as just one among a constellation of variations, the Waring problem of writing a homogeneous polynomial as a minimal sum of powers of linear homogeneous polynomials, which translates algebraically into studying ideals of powers.

These topics will be approached from three points of view---algebra, combinatorics, and geometry---and the interactions between these perspectives will be developed. Participants will be invited to explore the evolution of the set of associated primes of higher and higher powers of an ideal. For ideals associated to a combinatorial object like a graph or hypergraph, one wishes to explain this evolution in terms of the original combinatorial objects. Similar questions concern understanding the Castelnuovo-Mumford regularity of powers of combinatorially defined ideals in terms of the associated combinatorial data.

From a more geometric point of view, one can consider how the relations between symbolic and regular powers can be interpreted in geometrical terms. Other topics to be studied include aspects of Waring type problems and symbolic powers of an ideal, for example, Waldschmidt constants, resurgences, and the persistence of associated primes. A significant feature of this school of research is that participants will be divided into small groups (say groups of 2 to 3) to work on open problems on topics related to the main lectures. The lecturers will mentor each group, with the larger goal of providing each group with the basis for a project leading to a publication of the results in a professional journal. 

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 March 31th, 2017. The Committee of  Pragmatic will decide about financial supports and admissions within April 15th, 2017.
Interested people who need more information about Pragmatic can contact any member of the local committee.

The Organization of Pragmatic 2017 will cover the boarding and lodging expenses of the participants which are not supported by their  institutions, but not the travel expenses.

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APPLICATION FORM TO PRAGMATIC 2017

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