Speaker: Sara Maggio

Title: Twisted (Co-)homology, two applications for Feynman integrals

Abstract: Twisted (co-)homology provides a natural mathematical framework for dimensionally regulated Feynman integrals. In this talk, I will begin with a brief introduction to the basic ideas of this framework. I will then discuss two recent developments. First, I will explain how intersection matrices can be used to constrain canonical, (epsilon-factorised), systems of differential equations, including examples beyond the polylogarithmic setting. Second, I will show how symmetries of Feynman integrals can be formulated and studied within twisted (co)homology. A central outcome is a formula for counting master integrals in the presence of symmetries. These results illustrate applications of twisted (co-)homology that go beyond its original use in deriving integration-by-parts relations.