From the main video with Holly Krieger at https://youtu.be/N92w4e-hrA4 --- Catch Holly on the Numberphile Podcast: https://youtu.be/QmfQQzjpdpM The Dynamical Uniform Boundedness Conjecture. More videos with Holly: http://bit.ly/HollyKrieger Holly's website: https://www.dpmms.cam.ac.uk/~hk439/ She is the Corfield Lecturer at the University of Cambridge as well as a Fellow at Murray Edwards College. Go deeper with this technical paper: https://doi.org/10.1155/S1073792894000127 NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Animation by Pete McPartlan Support us on Patreon: http://www.patreon.com/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ A run-down of Brady's channels: http://www.bradyharan.com Sign up for (occasional) emails: http://eepurl.com/YdjL9