BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:!!!! ANNULÉ !!!! Perpetuants -- A lost treasure
DTSTART;VALUE=DATE-TIME:20200316T151500Z
DTEND;VALUE=DATE-TIME:20200316T161500Z
DTSTAMP;VALUE=DATE-TIME:20200921T002416Z
UID:indico-event-5546@indico.math.cnrs.fr
DESCRIPTION:Perpetuant is one of the several names invented by J. J. Sylv
ester. It appears in one of the first issues of the American Journal of Ma
thematics which he had founded a few years before. It is a name which wi
ll hardly appear in a mathematical paper of the last 70 years. \n\nWe wer
e surprised to find an entry in Wikipedia where it is mentioned that the f
ollowing beautiful result was conjectured by MacMahon in 1884 and proved
by \\name{Emil Stroh} in 1890.\n\n \n\nTHEOREM.\n\nThe dimension of the s
pace of perpetuants of degree $k>2$ and weight $g$ is the coefficient of $
x^g$ in\n\n \n\n${\\frac {x^{2^{k-1}-1}}{(1-x^{2})(1-x^{3})\\cdots (1-x
^{k})}}$\n\nFor $k=1$ there is just one perpetuant\, of weight 0\, and for
$k=2$ the number is given by the coefficient of $x^g$ in $x^2/(1-x^2)$.
\n\n \n\nWe will start with a short history of Classical Invariant Theory
of binary forms\, showing why the formula above comes as a surprise.\n\nW
e will explain the notion since it still has some mathematical interest\,
and also \\name{Stroh}'s proof which is quite remarkable and in a way ve
ry modern. With our method we are even able to exhibit a {\\em basis of pe
rpetuants} which is definitely a new result. \n\n(joint work with Claudio
Procesi)\n\nhttps://indico.math.cnrs.fr/event/5546/
LOCATION:UCBL-Braconnier Salle Fokko
URL:https://indico.math.cnrs.fr/event/5546/
END:VEVENT
END:VCALENDAR