C∗-Algebras of Self-Similar Groupoid Actions on Higher-Rank Graphs

A group action can be thought of as a group’s elements permuting the elements—or letters—of a finite set. A self-similar group action is a group action acting on the set of finite words
constructed from a finite set satisfying a condition relating parts of the group to the whole. In particular, we can associate C*-algebras to these actions and generalise the notion of group actions to graphs. This project aims to continue the study of self-similar actions and attempt to extend the theory to self-similar actions of groupoids of higher-rank graphs.

Tony Wang

The University of Sydney

Tony is a third-year student at the University of Sydney, studying a Bachelor of Science (Advanced) with a double major in Mathematics. He is intending on completing an Honours year in mathematics focusing on the field of partial differential equations, and hopes to get experience in the skills and knowledge necessary in academic research. He has been particularly interested in areas involving applications of (real and complex) analysis, functional analysis and the language of point-set topology. Given some free time away from university, Tony enjoys activities such as hiking, playing and watching tennis and fiddling around on his computer (non-productively!).

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