On equivalences between categories of representations

We explain some of the goals of modern representation theory, aiming at categorical methods. We develop one of the most astonishing invariant, Hochschild (co-)homology and we explain on the example of the recent solution of a question due to Rickard how it is possible to reduce fairly abstract questions to explicit methods finally solved by computers.We explain some of the goals of modern representation theory, aiming at categorical methods. We develop one of the most astonishing invariant, Hochschild (co-)homology and we explain on the example of the recent solution of a question due to Rickard how it is possible to reduce fairly abstract questions to explicit methods finally solved by computers.