20 October ~ D. Michailidis “Tensor Triangular Geometry”

In pure mathematics, we usually want to study the properties and the structure of an
algebraic, geometric or topological object. In order to study the relation between the object
and other similar objects or study some of its invariants we pass from the level of the abelian
categories to the level of the triangulated categories. In 2004 Paul Balmer inspired the attachment
of a topological space, the so called Balmer’s spectrum, to an abstract tensor triangulated
category K. Tensor triangular geometry is the study of the Balmer’s spectrum. The talk is
divided in three parts. First of all we will give two basic examples of tensor triangulated categories
coming from the Representation Theory and the Commutative Algebra. Secondly we will
present the basic points of Balmer’s theory and finally we will apply the results of the theory
into the distinguished examples of the first part.