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Noncommutative triangulated surfaces

Le : 08/10/2013 10h00
Par : 10h - Vladimir Retakh (Rutgers University, USA )
Lieu : I 103
Lien web :
Résumé : Triangulated surfaces play an important role in the theory of commutative cluster algebras. I will present a theory of noncommutative triangulations of oriented surfaces and show its relation to noncommutative Laurent phenomenon. This gives a foundation of noncommutative cluster theory of these surfaces. A surprising byproduct is a new topological invariant of closed oriented surfaces with punctures. Another application is a solution of a conjecture by Kontsevich: a proof of Laurentness and positivity of a noncommutative recursion. This is a joint work with Arkady Berenstein.