Speaker
Description
The relationship between unit leading singularities and canonical differential equations has played a central role in modern multi-loop calculations. While this connection is well understood for polylogarithmic integrals, its extension to more general classes of functions has remained unclear.
In this talk, I will present a generalized notion of leading singularities that naturally extends to elliptic and more complicated geometries. The construction explains why new transcendental functions necessarily appear in canonical bases beyond polylogarithms and shows how they can be identified through a generalized integrand analysis going beyond the $\epsilon=0$ limit. Once the leading singularities are properly normalized, the corresponding master integrals satisfy $\epsilon$-factorized differential equations in complete analogy with the polylogarithmic case.
This analysis provides a systematic framework for identifying canonical master integrals beyond polylogarithms, which are relevant to future high-precision calculations. I will illustrate the general concepts with explicit examples, starting with the simplest beyond-polylogarithmic example, namely, elliptic curves, and progressing to more general Calabi-Yau geometries.