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Mathematical Research at the University of Cambridge


I will show that Intersection Theory (for twisted de Rham cohomology) rules the algebra of Feynman integrals. In particular, I will address the problem of the direct decomposition of Feynman integrals into a basis of master integrals, showing that it can by achieved by projection, using intersection numbers for differential forms. After
introducing a few basic concepts of intersection theory, I will show the application of this novel method, first, to special mathematical functions, and, later, to Feynman integrals, also explaining how differential equations and dimensional recurrence relations for master Feynman integrals can be directly built by means of intersection
numbers. The presented method exposes the geometric structure beneath Feynman integrals, and offers the computational advantage of bypassing the system-solving strategy characterizing the standard reduction algorithms, which are based on integration-by-parts identities.
Examples of applications to multi-loop graphs contributing to multiparticle scattering, involving both massless and massive particles are presented.
(based on: arXiv:1810.03818, arXiv:1901.11510, arXiv:1907.02000)

Further information


Jan 23rd 2020
16:00 to 17:00


MR19 (Potter Room, Pavilion B), CMS


Pierpaolo Mastrolia (Padova)


HEP phenomenology joint Cavendish-DAMTP seminar