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Graphs are combinatorial objects that sit at the core of mathematical intuition. They appear in numerous situations all throughout Mathematics and have often constituted a source of inspiration for researchers. A striking instance of this can be found within the classes of graph C*-algebras and of Leavitt path algebras. These are classes of algebras over fields that emanate from different sources in the history yet quite possibly have a common future. Let E be a graph, i.e. a collection of vertices and edges that connect them. Very roughly, the process by which a C*-algebra is associated to E consists of decorating the vertices with orthogonal projections on a Hilbert space H and the edges by suitable operators. The ensuing C*-subalgebra of the bounded linear operators B(H) is then the graph C*-algebra C*(E). The Leavitt path algebras, denoted L(E), are the algebraic siblings of the aforementioned graph C*-algebras and are constructed over an arbitrary field (whereas here C*-algebras will always be over the complex numbers). Both classes of algebras, L(E) and C*(E), share a beautiful interplay between highly visual properties of the graph and algebraic/analytical properties of the corresponding underlying graphs. AIM: The main aim of this Research School is to bring postgraduates and young PhDs of mathematics in Turkey and in the countries around Turkey into the field of Leavitt path algebras and C*-algebras.

Songül Esin: songulesin@gmail.com