The Mathematics of Linear Relations between Feynman Integrals

For the precise prediction of observables at particle colliders such as the LHC, the computation of a large number of Feynman integrals is indispensable. A crucial step in these computations is the reduction to a small set of master integrals by exploiting linear relations.

In the standard approach such relations are derived from the famous integration-by-parts identities in momentum space and combined in Laporta's algorithm. Such reductions can easily grow too large to be executed with reasonable computer resources. Motivated by this problem, many new ideas on efficient reductions of Feynman integrals were presented in the recent literature. This workshop is dedicated to the mathematical techniques behind these developments, including finite field techniques, Gröbner bases, Milnor numbers, unitarity cuts and syzygy computations. In particular, techniques from algebraic geometry and the theory of D-modules have provided new insights. In an attempt to boost the exchange of ideas and the development of advanced methods, this workshop brings together mathematicians with relevant expertise, physicists with experience in Feynman integral reductions and specialists on computer algebra tools.