The first result we discuss states that the category of representations of the Kronecker algebra is derived equivalent to the category of coherent sheaves over the projective line.
We then study the construction of exact model structures together with the connections to cotorsion pairs and approximation theory. We discuss several applications, including the construction of monoidal model structures for the derived category of quasi-coherent sheaves of modules over a scheme. This part of the course is based on the following paper
Jan Stovicek, Exact model categories, approximation theory, and cohomology of quasi-coherent sheaves, in Advances in Representation Theory of Algebras (ICRA Bielefeld, Germany, 8-17 August, 2012), EMS Series of Congress Reports, European Mathematical Society Publishing House.
In January 2016, the reading course is complemented by a lecture
Discrete Derived Categories delivered by David Pauksztello,University of Manchester.
Calendar (November 2015 - February 2016)
Moreover, there will be the following lecture series of the PhD-School
Trento - Verona
Lecture series in April
Set theoretic methods in module theory
by Jan Trlifaj,Charles University Prague
April 10-18, 2016
Model Theoretic and Functor Theoretic Methods in Representation Theory
by Mike Prest,University of Manchester
April 3-16, 2016
Tentative schedule (April 2016)