The 2016 Nobel Prize in physics has been awarded to David Thouless from the University of Washington, Duncan Haldane from Princeton University, and to Michael Kosterlitz from Brown University. Their work involved using the mathematical field to look at unusual states of matter, such as superconductors and superfluids. This work will give rise to new developments in material science and electronics, including in quantum computing.

In 1980, the consensus as that superconductivity could not occur in thin layers, but Thouless and Kosterlitz showed that was wrong and used topology to explain why. They found that thin conductive layers could actually appear in materials by taking the form of discrete topological steps. Duncan Haldane also explains the magnetic properties of some materials. Initially the work "seemed very abstract" said Haldane, but as time went by more and more properties could be explained by topology.

Hello Yonathan,

Their work involved by using the mathematical (...) superconductors and ~~superfluids~~super-fluids.

~~This~~ Those/these work will give to rise ~~to~~a new developments in material ...

but Thouless and Kosterlitz showed that (need subject/pronoun ) was wrong and used ...

... layers could actually appear in materials by taking the form of discrete topological steps (need verb after gerund) so you can write: by taking the form of discrete has needed in topological steps

Duncan Haldane also ~~explains~~explained (past tense) the magnetic properties ...

hope these help