Priyanga Ganesan: [WS2] Insplitting in Textile Systems and Rank-2 Graphs

Speaker
Priyanga Ganesan, University of California San Diego

Abstract
The study of directed graphs, symbolic dynamics, and graph C*-algebras has led to many fruitful interactions in the classical setting. However, much less is known about their quantum counterparts. One possible approach toward developing quantum analogues is through the study of higher-dimensional graph structures such as Textile Systems and Rank-2 graphs. Textile systems are constructed by weaving together two directed graphs via graph homomorphisms and provide a useful framework for studying two-dimensional symbolic dynamical systems. Rank-2 graphs, on the other hand, are combinatorial objects that may be viewed as two-dimensional generalizations of directed graphs. In this talk, I will present a connection between the graphical move of insplitting in textile systems and the corresponding C*-algebraic notion of insplitting for Rank-2 graphs. This work is intended to serve as an initial step toward the future development of quantum analogues of higher-rank graphs, quantum shift spaces, and their associated operator algebras.