Geometria Complessa e Geometria Differenziale

PRAGMATIC 2017

created by daniele on 18 Feb 2017

19 jun 2017 - 7 jul 2017

Catania

Pragmatic 2017
(First announcement)

Catania, Italy
June 19th - July 7th, 2017
(arrival date June 18th; departure date July 8th)

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

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

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 an application form, available at http://www.dmi.unict.it/~pragmatic/docs/Pragmatic2017-1Ann.html which should be sent to the following address:

E-mail: pragmatic (AT) 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 or write to the above e-mail address.

Further information and application form at:

http://www.dmi.unict.it/~pragmatic/docs/Pragmatic2017-1Ann.html