Trying to understand the Hubbard model: Recent theoretical developments

Transition metal compounds are a large class of materials with fascinating properties and high application potential. Their theoretical
 description is based on a rather simple model, the Hubbard model, which is believed to comprise many qualitative aspects of the physics of this material class.

While having a simple structure, the Hubbard model has been a tremendous challenge to several generations of theoreticians since the early 60s of  the last century. Only during the past 10 years, the development of
 novel theoretical tools and the strong increase in computer power has
 caused a strong increase of our knowledge about this model.
 In my lecture I will introduce the basic concepts behind the Hubbard
 model and the present state-of-the-art methods to obtain insight into  its physical properties. As particular example I will present recent results on the Mott-Hubbard metal-insulator transition and spectral
 properties accompanying it.