Graph C*-algebras are analytical objects blessed with a tangible structure and classification theory derived from their combinatorial origins. Through the analysis of directed graphs, including higher-rank graphs or quantum graphs, one can visualize and explore them in intuitive ways lacking elsewhere. They serve as strikingly efficient models for key open problems in noncommutative geometry and topology, as well as in C*-dynamical systems. They also provide a focal point for the much-needed extension of the celebrated Elliott classification program to non-simple C*-algebras.

The main research objectives behind the proposed conference concern the classification, symmetry, structure and noncommutative metric geometry of operator algebras. The innovation in our approach comes from our emphasis on the ubiquitous class of graph C*-algebras, and through combination of ideas from many fields of research: unbounded operator theory, metric topology, classification by K-theory, KK-theory, and combinatorial and topological properties of graphs and groupoids. Here the key observation is that graphs provide convenient models for C*-algebras which one can visualize and explore in intuitive ways not generally avaliable, and yield manageable K-theoretical invariants. Such invariants are crucial for the celebrated Elliott classification program and studying the structure of corresponding operator algebras. This program was famously completed for simple C*-algebras in recent years, but the much-needed progress in extending the classification program to the non-simple cases relevant here requires deeper understanding of the relationship between combinatorics and invariants of operator algebras.