BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tobias Jäger (Friedrich Schiller University Jena) DTSTART:20261103T130000Z DTEND:20261103T140000Z DTSTAMP:20261026T125301Z UID:OWNS/173 DESCRIPTION:Title: S tructure theory of (multivariate) mean equicontinuous minimal systems\ nby Tobias Jäger (Friedrich Schiller University Jena) as part of One Worl d Numeration seminar\n\n\nAbstract\nWe review recent progress in the struc ture theory of topological dynamics\, which has led to a classification of mean equicontinuous minimal systems both in the univariate and multivaria te case. It was first shown by Downarowicz and Glasner in 2015 (building o n previous work by Li\, Tu and Ye) that a minimal topological dynamical sy stem is mean equicontinuous if and only if it is uniquely ergodic and a to po-isomorphic extension of its maximal equicontinuous factor (MEF)\, meani ng that the topological factor map is at the same time a measure-theoretic isomorphism between the two systems. Subsequently\, further subclasses de fined by dynamical properties (namely frequent stability and diam mean equ icontinuity) where equivalently characterised by their extension structure s over the MEF (almost one-to-one and regular\, respectively). Other dynam ical properties like nullness or tameness\, can then be related to the res ulting hierarchy (they both fall in the regular extension case). Moreover\ , a topological invariant named amorphic complexity turned out to be taylo r-made for the application to mean equicontinuous systems and allows to di stinguish conjugacy classes of a large number of examples\, including cons tant length substitutions and inflation tilings.\n\nMore recently\, this t heory has been successfully extended to the multivariate case: a minimal t opological dynamical system is mean m-equicontinuous if and only if it is an m-to-one topomorphic extension of its MEF\, and similarly frequent m-st ability corresponds to an almost m-to-one extension structure and diam mea n m-equicontinuity corresponds to m-regularity. The latter is also implied by m-tameness.\n\nThe talk aims to give an overview of these recent advan ces\, which are the result of the efforts of a broader community. Specific results by the speaker were obtained in joint work with Felipe Garcia-Ram os and Xiangdong Ye\, Eli Glasner and Christian Oertel\, Gabriel Fuhrmann\ , Maik Gröger and Dominik Kwietniak as well as Jonas Breitenbücher\, Lin o Haupt and others.\n LOCATION:https://researchseminars.org/talk/OWNS/173/ END:VEVENT END:VCALENDAR