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SUMMARY:An Update on Algebraic Hypergeometric Series (Remote)
DTSTART;VALUE=DATE-TIME:20211201T155000Z
DTEND;VALUE=DATE-TIME:20211201T164000Z
DTSTAMP;VALUE=DATE-TIME:20220529T025447Z
UID:indico-contribution-5971@indico.math.cnrs.fr
DESCRIPTION:Speakers: Maxim Kontsevich (IHES)\nAlgebraic hypergeometric se
ries in one variable were classified in 1989 by F. Beukers and G. Heckman\
, in terms of finite complex reflection groups. Recently\, K. Penson obser
ved that one of such series is a generating series of a probability densit
y with compact support\, given again by an algebraic function. Then togeth
er with N. Behr\, G. Duchamp and G. Koshevoy\, we found that this is a gen
eral phenomenon. The proof is an immediate application on an explicit inte
gral by Bateman and Erdélyi.The probability density is so called Meijer
’s G-function\, which the unique solution of the hypergeometric differen
tial equation with the pure ramification at point 1. I will speak about it
\, and also on the genus zero property of the corresponding planar algebra
ic curve.\n\nhttps://indico.math.cnrs.fr/event/7040/contributions/5971/
LOCATION:Le Bois-Marie Centre de conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/7040/contributions/5971/
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