Analytic Computation of Multi-loop Feynman Integrals for Higher-order QCD Corrections

In this talk, I will discuss the technical challenges in analytic computations of multi-loop integrals that appear in higher-order perturbative computations. I will explain the techniques for computing integrals with massive internal propagators needed for two-loop QCD corrections for Higgs decays and NNLO QCD corrections for \(t \bar{t} j\) production. The inclusion of massive internal propagators often lead to a more complicated class of function space, which will be another highlight of my talk.