The leitmotif for the IMPRS Mathematics in the Sciences is mathematical research with applications to the physical and life sciences. The topics of PhD theses in the IMPRS have to contribute to applications of the mathematical sciences with a genuine mathematical interest. Broadly categorizing the type of subject areas which have contributed questions of that type in the past for the IMPRS, these have been:

• microstructure and many particle systems primarily in classical physics;
• dynamical systems - discrete, continuous, deterministic and stochastic - in physics and the life and neuro sciences;and
• geometric aspects of the fundamental interactions investigated in theoretical physics.

This is a wide area and in the IMPRS we try to acquaint the PhD students with the main lines of research not only directly related to their thesis but also in neighboring mathematical fields. As a consequence, education within the IMPRS is characterized by the contrary goals of offering a solid knowledge in science as a whole and the naturally specialized research leading to a thesis. This turns out to create an inspiring and vivid atmosphere for research covering Mathematics in the Sciences.

This ambitious approach needs a strong grounding in the local research area and certainly, Leipzig is the correct place for this graduate school. Not only does the IMPRS fit the expertise of the MPI for Mathematics in the Sciences but it is also a field of research with a strong local community - depending on the specific subject in different institutes or departments of Leipzig University. Since the range of mathematics needed for this program is rather broad (among others geometry, partial differential equations, functional analysis, stochastics, discrete mathematics) and at the same time the range of applications is rather varied (theoretical physics, materials sciences, life sciences etc.) three institutes of Leipzig University are teaming up with the MPI for the IMPRS.

The Mathematical Institute has a long standing history in research in mathematics with a focus on real world applications. Currently, the faculty consists of about 20 professors and covers a broad range of mathematical topics and fields. The institute offers studies in mathematics (diploma), economathematics (diploma) and math teaching (Staatsexamen). Many of the advanced courses of the curriculum for the diploma in mathematics are also suitable for PhD students.

The Institute for Computer Science offers studies in computer science (Bachelor and Master) and computer science teaching (Master). It runs the DFG-Research Training group 1763 "QuantLA - Quantitative Logics and Automata" jointly with TU Dresden. Of special interest for the scope of the IMPRS is the group of bioinformatics of Peter Stadler.

The Institute for Theoretical Physics is part of the Physics Department of Leipzig University. It is responsible for the education in theoretical physics in several degree programs (Bachelor and Master). Research in this institute focuses on several topics in theoretical physics, in particular quantum gravity and quantum field theory, statistical physics, and theory of condensed matter.

The research field in the IMPRS is going to be divided into four main topics. These topics are

• Analysis,
• Geometry,
• Physics, and
• Stochastics and Discrete Structures.

Obviously, these topics are not disjoint and there will be a vivid interaction both between PhD students of different topics as well as between scientific members of the IMPRS. For details see the short information of the corresponding research direction.