BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gabriel Fuhrmann (Imperial College London) DTSTART:20200605T081500Z DTEND:20200605T094500Z DTSTAMP:20260423T021750Z UID:DSSUJ/5 DESCRIPTION:Title: So me recent progress on tameness in minimal systems\nby Gabriel Fuhrmann (Imperial College London) as part of Dynamical systems seminar at the Jag iellonian University\n\nLecture held in 1016.\n\nAbstract\nTameness is a n otion which--very roughly speaking--refers to the\nabsence of topological complexity of a dynamical system. The last\ndecades saw an increased inter est in tame systems revealing their\nconnections to other areas of mathema tics like Banach spaces\,\nsubstitutions and tilings or even model theory and logic. In this\ntalk\, we will assume a dynamical systems perspective. \n\nHuang showed that\, given a minimal system\, tameness implies almost\n automorphy [1]. That is\, after discarding a meagre set of points\, the\nf actor map of a tame minimal system to its maximal equicontinuous\nfactor i s one-to-one. This structural theorem got recently extended to\nactions of general groups by Glasner [2].\n\nIn a collaboration with Glasner\, Jäge r and Oertel\, we could further\nimprove this result by showing that tame minimal systems are actually\nregularly almost automorphic [3]. In this ta lk\, we will show a closely\nrelated statement which\, however\, is way ea sier to prove: every\nsymbolic almost automorphic extension of an irration al rotation whose\nnon-invertible fibres form a Cantor set is non-tame. We will further\ndiscuss some related results from a collaboration with Kwie tniak [4].\nFinally\, if time allows\, we will come to discuss tameness in \nsubstitutive subshifts and more general classes of Toeplitz flows [5].\n \nAll (non-standard) notions will be introduced in the talk. In other\nwor ds: we prioritise accessibility over the number of results to be\ndiscusse d.\n\n[1] W. Huang\, Tame systems and scrambled pairs under an abelian gro up\naction\, Ergodic Theory Dynam. Systems 26 (2006)\, 1549-1567.\n\n[2] E . Glasner\, The structure of tame minimal dynamical systems for\ngeneral g roups\, Invent. Math. 211 (2018)\, 213-244.\n\n[3] G. Fuhrmann\, E. Glasne r\, T. Jäger\, C. Oertel\, Irregular model sets\nand tame dynamics\, arXi v:1811.06283\, (2018)\, 1-22.\n\n[4] G. Fuhrmann\, D. Kwietniak\, On tamen ess of almost automorphic\ndynamical systems for general groups\, Bull. Lo n. Math. Soc. 52 (2020)\,\n24-42.\n\n[5] G. Fuhrmann\, J. Kellendonk\, R. Yassawi\, work in progress.\n LOCATION:https://researchseminars.org/talk/DSSUJ/5/ END:VEVENT END:VCALENDAR