BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Simon Machado (the University of Cambridge) DTSTART:20220324T161500Z DTEND:20220324T173000Z DTSTAMP:20260423T021927Z UID:NEDNT/44 DESCRIPTION:Title: S uperrigidity and arithmeticity for some aperiodic subsets in higher-rank s imple Lie groups\nby Simon Machado (the University of Cambridge) as pa rt of New England Dynamics and Number Theory Seminar\n\nLecture held in On line.\n\nAbstract\nMeyer sets are fascinating objects: they are aperiodic subsets of Euclidean spaces that nonetheless exhibit long-range aperiodic order. Sets of vertices of the Penrose tiling (P3) and Pisot-Vijarayaghava n numbers of a real number field are some of the most well-known examples. In his pioneering work\, Meyer provided a powerful and elegant characteri sation of Meyer sets. Years later\, Lagarias proved a similar characterisa tion starting from what seemed to be considerably weaker assumptions.\nA f ascinating question asks whether Meyer’s and Lagarias’ results may be extended to more general ambient groups. In fact\, a first result in that direction was already obtained in Meyer’s work: he proved a sum-product phenomenon which\, implicitly\, boiled down to a classification of Meyer s ets in the group of affine transformations of the line.\nI will talk about a generalisation of both Meyer’s and Lagarias’ theorems to discrete s ubsets of higher-rank simple Lie groups. I will explain how this result ca n be seen as a generalisation of Margulis’ arithmeticity theorem and how it can be deduced from Zimmer’s cocycle superrigidity. We will see that \, surprisingly\, Pisot-Vijarayaghavan numbers appear naturally in this co ntext too.\n LOCATION:https://researchseminars.org/talk/NEDNT/44/ END:VEVENT END:VCALENDAR