Sheaves, Cohomology, and Data

This is a talk about Applied Mathematics -- the taming and tuning of mathematical structures to the service of problems in the sciences. The Mathematics to be harnessed comes from algebraic topology: it is sheaf theory, the study of local-to-global transitions. The applications I will focus on are in the engineering sciences, but are not fundamentally restricted to such. We will begin with a gentle introduction to sheaves and proceed to their many uses: in sensing, coding, optimization, and inference. No background in sheaves needed, though a little elementary knowledge of algebraic topology (such as homology) might be helpful.