Connecting Measures with Sheaves

Our interest is in exploring a connection between measures and sheaves. The goal for studying such a connection is twofold: First, this would provide the potential for defining a probabilistic framework for sheaves. Second, we hope that this will pave the way for using sheaves as a stochastic vehicle for statistical studies such as MCMC sampling and modeling algebraic random walks.

We will present some very preliminary ideas and thoughts on how to construct such a connection, and invite an open discussion on this problem. This is work in progress with, and will be presented together with, Nicolas Berkouk.