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SUMMARY:Dynamical Systems Seminar – Dan Rust (The Open University)
DESCRIPTION:\nRandom Pisot substitutions and their Rauzy fractals\nAbstract
 : The Pisot conjecture is a long-standing open question concerning the dyn
 amical spectrum of subshifts associated with Pisot substitutions. One form
 ulation of the conjecture can be stated in terms of the so-called Rauzy fr
 actal for the substitution\, which is the attractor of a graph-directed it
 erated function system that can be written purely in terms of data coming 
 from the substitution. Random substitutions generalise substitutions and c
 an be used to interpolate between them\, allowing properties of one substi
 tution to inform properties of another. In this talk\, we will introduce R
 auzy fractals for Pisot random substitutions and results concerning natura
 l measures that can be defined on the attractor. By studying these measure
 s\, we are able to prove an analogue of a multi-tiling result for Rauzy fr
 actals but in the random setting\, hinting at potential new tools for tack
 ling the Pisot conjecture using probabilistic methods. This is joint work 
 with Philipp Gohlke\, Andrew Mitchell and Tony Samuel.\n
URL:https://www.imperial.ac.uk/events/206186/dynamical-systems-seminar-dan-
 rust-the-open-university/
DTSTART;TZID=Europe/London:20260224T130000
DTEND;TZID=Europe/London:20260224T140000
LOCATION:145\, Huxley Building\, South Kensington Campus\, Imperial College
  London\, London\, SW7 2AZ\, United Kingdom
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