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Operator Algebra and Noncommutative Geometry Seminar Series
June 21, 2017 @ 3:30 pm - June 22, 2017 @ 4:30 pm
Mauldin-Williams graphs and their operator algebras
Michael Mampusti (University of Wollongong)
Time and Date: 3:30pm-4:30pm Thursday, 15 June 2017
Location: Room 39C.174
In this talk, we explore the origins of the study of Mauldin-Williams graphs, and the operator algebras associated to them. We first look at iterated function systems, introduced by Hutchinson, as a mathematical model for the study of fractals, using the Sierpinski triangle as one of our examples. We then realise Mauldin-Williams graphs, introduced by Mauldin and Williams, as a generalisation of iterated function systems, and briefly look how we can study substitution tilings in this framework. From here, we look some of the operator algebras associated to Mauldin-Williams graphs by Ionescu, and Ionescu and Watatani, and finish off with why these algebras might be interesting by calculating their KMS state structure.