New results in the dimension theory of continued fraction Cantor sets
Ergodic Theory and Dynamical Systems Seminar
26th November 2020, 4:30 pm – 5:30 pm
Online via Zoom, Link will be released to the seminar email list shortly before the seminar. Please contact the organisers for more information. You can subscribe at https://www.jiscmail.ac.uk/cgi-bin/webadmin?A0=BRISTOLETDSSEMINAR
Continued fractions have provided a natural playground for several developments in number theory, analysis, dynamics and probability theory. We highlight recent advances, obtained with David Simmons, Lior Fishman, and Mariusz Urbanski, in the dimension theory of continued fraction Cantor sets – a rich research seam pioneered around ninety years ago by Jarnik and Good. The talk will be accessible to graduate students and beyond who might be interested in some convex combo of analysis, dynamics, fractals, and number theory. Most importantly, I hope to present a sampling of open questions and research directions that await exploration.