August 28 , 2008
Speaker: Andrei Zelevinsky (Northeastern University)
Title of talk: "Quivers with potentials and their representations"
Abstract: A quiver is a finite directed graph, that is, a finite set of vertices some of which are joined by arrows. A quiver representation assigns a finite-dimensional vector space to each vertex, and a linear map between the corresponding spaces to each arrow. The theory of quiver representations is a beautiful and well-developed field. A fundamental role in this theory is played by Bernstein-Gelfand-Ponomarev reflection functors associated to every source or sink of a quiver. In an ongoing joint work with Harm Derksen and Jerzy Weyman we extend these functors to arbitrary vertices. This construction is based on a framework of quivers with potentials; their representations are quiver representations satisfying relations of a special kind between the linear maps attached to arrows. The motivations for this work come from several sources: superpotentials in physics, Calabi-Yau algebras, cluster algebras. However no special knowledge will be assumed in any of these subjects, and the exposition should be accessible to graduate students.

September 18, 2008
Speaker: Professor Xiao-Li Meng, Harvard University
Title of talk: Some wavelet applications in Statistics