Abstract: In 1969 D.V. Anosov and A. Katok came up with a recipe, now
known as the 'approximation by conjugation' method or the 'Anosov-Katok'
method to construct examples of smooth transformations in ergodic theory.
Though these diffeomorphisms are often viewed as "exotic if not
pathological", they have managed to gain a considerable amount of
attention in recent years, specially in regards to the isomorphism
problems, smooth realization problems, and many other problems from
classical smooth ergodic theory. In this talk we will have a description
of this technique and talk about some applications.