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Topological quantum computation is based on the possibility of the realization of some TQFTs in Nature as topological phases of quantum matter.  Theoretically, we would like to classify topological phases of matter, and experimentally, find non-abelian objects in Nature.  We will discussion some progress for a general audience.

 

In this talk we will discuss how C*-algebras can be identified and characterised in terms of certain cosheaves with self-action. The reason we are interested in such a study is it to try and give a rigorous mathematical derivation of the axioms of quantum theory. In particular, many of the standard axioms for C*-algebras have unclear physical and operational meaning, but by defining an equivalence of categories between C*-algebras and cosheaves with self-action, we believe that these axioms can acquire a clear operational meaning. So far, however, we have only managed to show that every C*-algebra becomes a cosheaf with self-action, but we don't know whether the converse holds as well. This work is done in collaboration with Tobias Fritz.