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Seminario MALGA Padova Verona - Moduli Algebre Anelli

Martedi' 28 giugno 2011 - G. Cerulli Irelli, P. Jørgensen

ARGOMENTI: Seminari

Martedi' 28 giugno 2011 a Padova, in Aula 2BC60 della Torre Archimede si terra' il prossimo incontro del Seminario Padova - Verona MALGA (moduli, algebre, anelli).

ore 15:00
Giovanni Cerulli Irelli
"Degenerate flag varieties and quiver Grassmannians"

ore 16:30
Peter Jørgensen (Newcastle University)
"Ptolemy diagrams and torsion pairs in cluster categories of Dynkin type A"

-Abstract Cerulli Irelli
In a recent preprint, in collaboration with Evgeny Feigin and markus Reineke, we noticed that the degenerate flag varieties introduced and studied by Feigin are indeed quiver Grassmannians, i.e. varieties of subrepresentations of a given quiver representation M of fixed dimension vector. In this talk we illustrate how this simple observation helps in the study of the geometry of degenerate flag varieties.

-Abstract Jørgensen
A Ptolemy diagram is a simple combinatorial object: A collection of diagonals in a polygon with the property that if the collection contains two crossing diagonals, then it also contains all other diagonals connecting end points of the crossing ones. They could have been defined at any point since antiquity but were in fact introduced recently, in an infinite version, by Puiman Ng. We give a new combinatorial description of (finite) Ptolemy diagrams, show how they parametrise torsion pairs in cluster categories of Dynkin type A, and count the number of such torsion pairs.

Rif. int. S. Bazzoni

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