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SUMMARY:Intersection Theory and Feynman Integrals - Pierpaolo Mastrolia (P
 adova)
DTSTART:20200123T160000Z
DTEND:20200123T170000Z
UID:TALK134923@talks.cam.ac.uk
CONTACT:Mathieu Pellen
DESCRIPTION:I will show that Intersection Theory (for twisted de Rham coho
 mology) rules the algebra of Feynman integrals. In particular\, I will add
 ress the problem of the direct decomposition of Feynman integrals into a b
 asis of master integrals\, showing that it can by achieved by projection\,
  using intersection numbers for differential forms. After\nintroducing a f
 ew basic concepts of intersection theory\, I will show the application of 
 this novel method\, first\, to special mathematical functions\, and\, late
 r\, to Feynman integrals\, also explaining how differential equations and 
 dimensional recurrence relations for master Feynman integrals can be direc
 tly built by means of intersection\nnumbers. The presented method exposes 
 the geometric structure beneath Feynman integrals\, and offers the computa
 tional advantage of bypassing the system-solving strategy characterizing t
 he standard reduction algorithms\, which are based on integration-by-parts
  identities.\nExamples of applications to multi-loop graphs contributing t
 o multiparticle scattering\, involving both massless and massive particles
  are presented.\n(based on: arXiv:1810.03818\, arXiv:1901.11510\, arXiv:19
 07.02000)\n\n\nThe slides of the presentation can be found "here":http://w
 ww.hep.phy.cam.ac.uk/~conference/Mastrolia_24_01_2020.pdf
LOCATION:MR19 (Potter Room\, Pavilion B)\, CMS
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