Treatment of integrals with singular geometries in the exponential-periods framework

Develop methods within the exponential periods framework to handle integrals whose underlying geometric spaces are singular, including the construction of appropriate (co)homologies, local systems, and intersection pairings that remain valid in the presence of singularities.

Background

The paper establishes an approach to interpret a wide class of integrals—such as Feynman and Pearcey-type integrals—as exponential periods, but smoothness plays a central role in the current constructions.

The authors identify extending these techniques to singular geometries as a key next step, noting that such cases present additional technical challenges and currently remain unresolved.