BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Sabre//Sabre VObject 4.5.8//EN CALSCALE:GREGORIAN BEGIN:VTIMEZONE TZID:Europe/Zurich X-LIC-LOCATION:Europe/Zurich TZURL:http://tzurl.org/zoneinfo/Europe/Zurich BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19810329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19961027T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:news1307@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20220425T100745 DTSTART;TZID=Europe/Zurich:20220428T170000 SUMMARY:Number Theory Web Seminar: Andrew Granville (Université de Montré al) DESCRIPTION:In 1878\, in the first volume of the first mathematics journal published in the US\, Edouard Lucas wrote 88 pages (in French) on linear r ecurrence sequences\, placing Fibonacci numbers and other linear recurrenc e sequences into a broader context. He examined their behaviour locally as well as globally\, and asked several questions that influenced much resea rch in the century and a half to come.\\r\\nIn a sequence of papers in the 1930s\, Marshall Hall further developed several of Lucas' themes\, includ ing studying and trying to classify third order linear divisibility sequen ces\; that is\, linear recurrences like the Fibonacci numbers which have t he additional property that $F_m$ divides $F_n$ whenever $m$ divides $n$. Because of many special cases\, Hall was unable to even conjecture what a general theorem should look like\, and despite developments over the years by various authors\, such as Lehmer\, Morgan Ward\, van der Poorten\, Bez ivin\, Petho\, Richard Guy\, Hugh Williams\,... with higher order linear d ivisibility sequences\, even the formulation of the classification has rem ained mysterious.\\r\\nIn this talk we present our ongoing efforts to clas sify all linear divisibility sequences\, the key new input coming from a w onderful application of the Schmidt/Schlickewei subspace theorem from the theory of diophantine approximation\, due to Corvaja and Zannier.\\r\\nFor further information about the seminar\, please visit this webpage [https: //www.ntwebseminar.org/]. X-ALT-DESC:

In 1878\, in the first volume of the first mathemat ics journal published in the US\, Edouard Lucas wrote 88 pages (in French) on linear recurrence sequences\, placing Fibonacci numbers and other line ar recurrence sequences into a broader context. He examined their behaviou r locally as well as globally\, and asked several questions that influence d much research in the century and a half to come.

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In a sequence of papers in the 1930s\, Marshall Hall further developed several of Lucas' themes\, including studying and trying to classify third order l inear divisibility sequences\; that is\, linear recurrences like the Fibon acci numbers which have the additional property that $F_m$ divides $F_n$ w henever $m$ divides $n$. Because of many special cases\, Hall was unable t o even conjecture what a general theorem should look like\, and despite de velopments over the years by various authors\, such as Lehmer\, Morgan War d\, van der Poorten\, Bezivin\, Petho\, Richard Guy\, Hugh Williams\,... w ith higher order linear divisibility sequences\, even the formulation of t he classification has remained mysterious.

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In this talk we present our ongoing efforts to classify all linear divisibility sequenc es\, the key new input coming from a wonderful application of the Schmidt/ Schlickewei subspace theorem from the theory of diophantine approximation\ , due to Corvaja and Zannier.

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For further information about the se minar\, please visit this webpage< /a>.

DTEND;TZID=Europe/Zurich:20220428T180000 END:VEVENT END:VCALENDAR