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SUMMARY:A hypergeometric view on banana integrals and beyond
DTSTART:20260305T120000Z
DTEND:20260305T130000Z
DTSTAMP:20260420T152400Z
UID:indico-event-11814@indico.mpp.mpg.de
DESCRIPTION:Speakers: Saiei Matsubara (Tohoku University)\n\n In the first
  part of this talk\, we study the holonomic system (= a system of differen
 tial equations with a finiteness property) M to which the banana Feynman i
 ntegral is subject. M is a special case of a more general class of D-modul
 es for which we coin the term "reciprocal A-hypergeometric system." We pro
 ve that M has holonomic rank (a.k.a. the number of master integrals) 2^{L+
 1}-1\, where L is the number of loops. Moreover\, we identify solutions of
  M with Lauricella's hypergeometric functions F_C. In the second part of t
 he talk\, we switch to the general reciprocal A-hypergeometric system. We 
 show that it is a natural matroid analogue of the Gelfand-Kapranov-Zelevin
 sky theory of A-hypergeometric systems by providing some results: it is ho
 lonomic\; it has an integral representation\; and its singular locus is pr
 ojectively dual to the reciprocal linear space.The first part is based on 
 joint work in progress with Giacomo Brunello (Scuola Normale Superiore)\, 
 Vsevolod Chestnov (Oxford)\, Wojciech Flieger (Padova\, OIST)\, Pierpaolo 
 Mastrolia (Padova)\, and Nobuki Takayama (Kobe)\; the second part is based
  on joint work in progress with Simon Telen (MPI MiS).\n\nhttps://indico.m
 pp.mpg.de/event/11814/
LOCATION:A.1.01 - Alps  Süd (MPP)
URL:https://indico.mpp.mpg.de/event/11814/
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