Description
Linear differential operators play a prominent role in the study of Feynman
integrals and related special functions. In this talk, I will discuss two complementary
aspects of this framework. First, I will describe an algorithm for constructing differential
operators that annihilate Feynman integrals and for deriving the associated Pfaffian
systems of first-order linear differential equations. Second, I will explain how singular limits
of Pfaffian systems can be studied systematically through restriction theory, leading to
asymptotic expansions near singular limits. As an illustration, I will show how these ideas
apply to the post-Newtonian expansion of gravitational waveforms.