Gelfand Duality and its Applications

The Gelfand Duality is an equivalence of categories between the category of commutative unital C*-algebras and the category of compact Hausdorff spaces. The talk will cover this equivalence of categories, some of the language needed to describe it (categories, C*-algebras), some generalisations and specialisations, and some interesting applications in harmonic analysis and group theory.