**Program:**

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
series on *
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

Program

April 10-18, 2016

*Model Theoretic and Functor Theoretic Methods in Representation
Theory*

by Mike
Prest,University of
Manchester

Program

April 3-16, 2016