In this talk I will review the appearance of periods as Feynman integral associated to classical and quantum scattering.
Using some specific examples, I will give a brief survey of the state of the art of the subject and describe in which physical quantities they arise.
The period matrix of a smooth complex projective variety encodes the isomorphism between its singular homology and its algebraic De Rham cohomology. Numerical approximations with sufficient precision of the entries of the period matrix allow to recover some algebraic invariants of the variety. Such approximations can be obtained from an effective description of the homology of the variety,...
A growing body of evidence suggests that the complexity of physical integrals is most naturally understood through geometry. Recent mathematical developments by Kontsevich and Soibelman [arXiv:2402.07343] have illuminated the role of exponential integrals as periods of twisted de Rham cocycles over Betti cycles, offering a structured approach to address this problem in a wide range of...