Due to the recent development of efficient algorithms and implementations, homology and cohomology theories have become useful tools in various branches of science and engineering. For example, electromagnetic modeling provides an interesting context to present a link between physical phenomena and homology and cohomology. Over the past twenty-five years a considerable effort has been invested by the computational electromagnetics community to develop fast and general techniques for potential design. Nevertheless, heuristic approaches seem still to be dominant in literature. During the talk a proof will be given showing that, for edge-element based finite element method, the first cohomology group generators are needed to make boundary value problem well defined. To conclude, efficient algorithmic techniques to compute cohomology group generators on various meshes (being arbitrary regular CW-complexes) will be presented together with results of electromagnetic simulations (this is joint work with Ruben Specogna).

If time permits, recent progress in distributed (co)homology computations will be discussed. As an example, a coverage problem in sensor network will be presented and distributed computation techniques used to solve it will be highlighted (joint work with Robert Ghrist, Mateusz Juda and Marian Mrozek).