Colloquium, part of the RTG2575 QFT-Colloquia series

Speaker: Ben Page, UGent and CERN

Title: Modern Algebra in Particle Physics

Abstract: In the quest to better understand the fundamental constituents of nature,
experimentalists at the Large Hadron Collider (LHC) measure high-energy particle
collisions of at unprecedented levels of precision. In order to use this data to
test the validity of the Standard Model of Particle Physics, it is essential to
have a theoretical description of the collision process at the corresponding
level of precision. Given the distinguished role that the strong force plays at
the LHC, this necessitates perturbative computations of “scattering
amplitudes” (sums of Feynman diagrams) to high loop orders. These calculations,
notoriously difficult due to the complex theoretical structure of QCD, place
formidable demands on both our conceptual and practical understanding of an
age-old friend: algebra. Indeed, algebraic descriptions of the involved Feynman
diagrams alone could nearly fill a university library.

In this talk, we dive into the modern world of how these feats of algebra are
undertaken in precision physics computations. We showcase how traditional
technical bottlenecks in computer algebra have been smashed with the
introduction of number theoretical methods and how the newly opened frontiers
drive us to develop a deeper, more geometrical, understanding of algebra.