|Date: Friday, February 22, 2013
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: Positivity and tameness in rank 2 cluster algebras
Abstract: A lot of recent activity in the theory of cluster algebras has been directed towards various constructions of "natural" bases. In a joint work with A.Zelevinsky and K.Lee we construct a new basis in any rank 2 cluster algebra following an approach developed by P.Sherman and A.Zelevinsky. This basis consists of a special family of indecomposable positive elements that we called greedy elements. Inspired by the work of K.Lee, R.Schiffler and D.Rupel, we give an explicit combinatorial description for the greedy elements using the language of Dyck paths. Furthermore, we show that the indecomposable positive elements form a basis if and only if the cluster algebra is tame (that is, of finite or affine type).
Speaker: Li Li
Institution: Oakland University
Event Organizer: Sergey Fomin