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SUMMARY:Feynman Integrals and Intersection Theory
DTSTART;VALUE=DATE-TIME:20190513T123000Z
DTEND;VALUE=DATE-TIME:20190513T133000Z
DTSTAMP;VALUE=DATE-TIME:20200401T122123Z
UID:indico-event-4567@indico.math.cnrs.fr
DESCRIPTION:I will show that Intersection Theory (for twisted de Rham coho
mology) rules the algebra of Feynman integrals. In particular I will addre
ss the problem of the direct decomposition of Feynman integrals into a bas
is of master integrals\, showing that it can by achieved by projection\, u
sing intersection numbers for differential forms. After introducing a few
basic concepts of intersection theory\, I will show the application of thi
s novel method\, first\, to special mathematical functions\, and\, later\,
to Feynman integrals on the maximal cuts\, also explaining how differenti
al equations and dimensional recurrence relations for master Feynman integ
rals can be directly built by means of intersection numbers. The presented
method exposes the geometric structure beneath Feynman integrals\, and of
fers the computational advantage of bypassing the system-solving strategy
characterizing the standard reduction algorithms\, which are based on inte
gration-by-parts identities. Examples of applications to multi-loop graphs
contributing to multiparticle scattering\, involving both massless and ma
ssive particles are presented.\n\nhttps://indico.math.cnrs.fr/event/4567/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/4567/
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