Intersection theory provides a unified framework for studying Feynman integrals and String amplitudes, capturing their linear and quadratic relations and enabling their reduction to a finite basis of master integrals. This is particularly important in multi-loop calculations, where direct evaluation is often unfeasible. While twisted de Rham cohomology is well suited to integrals with multivalued integrands, such as those arising in dimensional regularization, it does not fully capture cases with richer geometric structures, including singularities and nontrivial monodromy. In this talk, I will discuss a systematic construction of the relevant homology and cohomology groups that allows Feynman integrals and String amplitudes to be interpreted as exponential periods. Combined with analytic continuation in the dimensional regulator, this framework naturally incorporates wall crossing and Stokes phenomena and provides a precise count of master integrals.