# Mathematics Colloquia and Seminars

This talk will focus on the similarly-titled paper by Schwarz and Shapiro ( arXiv:0809.0086v1). In particular, we will discuss a homological generalization of integrals of the form $\int e^{f(x)} \omega$, where the domain of integration can be an arbitrary ring, $R$ (instead of $\mathbb{R}$). This will prove useful in light of certain "integrality conditions" preserved among such integrals. In a physical context, this homological definition of an integral may be loosely interpreted as a generalization of spatial coordinates to ring-valued quantities. We will begin with a brief review of the usual de Rham cohomology (with real coefficients) - hence, only very little familiarity with homology will be assumed.