Geometry MMA Seminar: Self-similar constructions of fractals by substitution

Speaker:  Sylvester Eriksson-Bique, University of Jyväskylä

Title:  Self-similar constructions of fractals by substitution

Abstract:  Substitution is a broad framework for describing and defining self-similar objects. In this talk, I will explain a particular way of doing this: Iterated Graph Systems. These are combinatorial analogues of iterated function systems and give a way of producing fractals with a number of interesting - and surprising - properties. While the idea for such constructions must be ancient, we only recently discovered that such constructions give solutions to old open problems in analysis on metric spaces. I will give a hint of these questions and the reason these examples are particularly well suited for these problems. We will also see that the framework describes many classical fractals, such as Laakso spaces and Laakso diamonds. The talk includes joint work with Riku Anttila and Guy C. David.

Time: Monday, November 25, 2024 – 10:30am-11:30am

Place: Exploratory Hall, Room 4106