A talk by Dr. Yann Palu from Universite de Picardie, Amiens France in our monthly “Mathematics Seminar” with following details.
Title: Cluster algebras and representation theory
Date: Monday, March 3, 2014
Time: 15.00 -16.00
Place: Ruang Rapat Gedung Matematika Labtek III ITB (ITN, Labtek III Building, Ruang Rapat)
Cluster algebras were introduced by Fomin and Zelevisky in their study of total positivity and canonical bases. Starting from an oriented graph, one can define the generators of a cluster algebra by means of an inductive operation called “mutation”. This unusual definition forces cluster algebras to satisfy several interesting properties, such as the Laurent phenomenon and positivity. The combinatorics underlying this mutation procedure turned out to appear in many different areas of mathematics: integrable systems, Poisson geometry, algebraic geometry, and representation theory of algebras. This talk will be an introduction to cluster algebras and an illustration of their basic properties with some small examples.
Another talk by same speaker in our bi-weekly “Algebra Seminar” with following details.
Title: An introduction to Caldero-Chapoton maps
Date: Wednesday, March 5, 2014
Time: 14.30 – 15.30
Place: Ruang Seminar I.2 Gedung Matematika Labtek III ITB (ITB, Labtek III Building, Ruang Seminar I.2)
Cluster algebras were introduced by Fomin and Zelevisky. They are defined by giving specific generators, called cluster variables. The Caldero-Chapoton map is an important tool in the theory of categorification of cluster algebras. It gives an “explicit” formula for the cluster variables of a cluster algebra associated with a quiver in terms of the representations of this quiver. The talk will be an introduction to the Caldero-Chapoto map for Jacobi-finite quivers and illustrated with examples.