We will talk about our contribution to a large project with the goal
of a self-consistent numerical simulation of the evolution of the
universe beginning soon after the Big Bang and ending with the
formation of realistic stellar systems like the Milky Way. This is a
multi-scale problem of vast proportions. It requires the development
of new numerical methods that excel in accuracy, parallel scalability
to the processes relevant in galaxy formation. These numerical methods
themselves require the development of mathematical theory in order to
guarantee the above mentioned requirements. in this talk we shall
focus on our contribution to this effort. This is joint work among
others with Volker Springel.
