Applications of Category Theory

 Ovsienko Serge  (Kiev Taras Shevchenko University)
In our lectures we will expose (relatively) new algebraic methods, which were effectively applied in surprisingly various branches of mathematics. We explain, how this phenomenon relates with a unifying role of the notion of a category and its generalizations. Especially, we fix our attention on the theory of descent and its applications. Besides, it will be shown, how such approach can lead us to the "representation-theoretic" point of view. We will give examples, how the methods above are used in algebraic and differential geometry, differential equations and physics.