Speaker
Description
In this talk, I present a general and powerful strategy for solving integration-by-parts (IBP) identities, which take the form of multivariable linear homogeneous relations among Feynman integrals. Our diagonalisation approach transforms the IBP system into effectively single-variable recurrence relations. This diagonal structure exposes the analytic behaviour of the reduction and provides a direct route to closed-form solutions, making it especially valuable when propagator powers are treated as abstract variables, such as in the Mellin representation, or when very high powers appear. As a by-product of this framework, I will also briefly discuss a more specialised variant, the triangularisation method, which adapts the diagonal strategy to QCD multi-loop reductions for improved computational efficiency. Together, these developments offer both conceptual clarity and significant computational gains for modern multi-loop calculations.
