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Twisted de Rham Cohomology and Physics Over a Ring

QMAP Seminar

Speaker: Pat Dragon, UC Davis
Location: 3106 MSB
Start time: Wed, Nov 25 2009, 4:10PM

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.