Modern Applications of Homology and Cohomology

(Co)homology theories, and more specifically algebraic structures on the cochain complex, have recently surfaced in unexpected areas of applied mathematics. The concrete interpretation of the cochain complex as a discretization of differential forms was a key insight of Thom and Whitney from the 1950s. This viewpoint has recently found new application in reinterpreting the families of forms that appear in computational fluid mechanics and electrodynamics. More generally, there has been striking advances relating the cochain complex to questions of stability in finite element and finite volume methods.

An area that has seen a lot of exciting recent development is applications of Hodge-De Rham theory. Several variants of this have been applied in new ways to obtain surprising results in a wide variety of disparate areas, including cognitive science, computer graphics and vision, game theory, machine learning, numerical PDE, voting theory, sensor networks, and statistical ranking.

This workshop will serve as a gathering place for all those interested in the applications of homology and cohomology theories to science and engineering. We intend to provide a forum for applied practitioners from diverse areas to share ideas and also to provide a venue for working algebraic topologists (pure mathematicians) to be exposed to applied problems. We hope that the wide array of backgrounds and intended applications will productively intermingle perspectives and methodology.