Mathematical structures of quantum systems: An algebraic, analytical and computational study. 

Mathematics provides us with a language in which to formulate the laws that govern the phenomena observed in nature. This language has proven to be both powerful and effective, and, the question of how reasonable this effectiveness may be aside, in trying to understand the basic laws of nature one is bound to use the tools that mathematics supplies.

A foundation of physics cannot be built solely on this ground, however; an even more essential ingredient is experiment, and any substantial progress in physics should eventually allow for predictions that can be tested experimentally. Nevertheless, the quest for a deeper understanding of fundamental physical issues, such the interactions among elementary particles or the structure of space-time, tends to lead to theories which are ever harder to put to observational tests.

In this situation, mathematical conciseness and internal consistency of a physical theory become increasingly important guidelines in the evolution of physics.

It is less evident what parts of mathematics are most relevant for the study of some given area of physics and whether or not the existing mathematical knowledge is already sufficient for addressing all problems within the area in question. In recent years, novel questions have merged in mathematical physics, notably in quantum field theory. Accordingly, additional areas of mathematics have become influential and, in turn, been influenced themselves by the developments in physics.

As a consequence, over the last two decades interactions between mathematicians and physicists have increased enormously, resulting in a fruitful cross-fertilization between different communities.

In studies of physical phenomena we want to discover hidden mathematical structures which govern underlying processes. These structures can be either known or new but in any case new studies in physics pose new mathematical problems even in old classical areas of mathematics. In its turn, studies of mathematical structures relevant to the physical phenomena lead to new developments of physical theories.

The aim of the platform is to provide an environment that stimulates the collaboration between mathematicians and theoretical physicists. A number of defined projects linked with each other is proposed and a joint mathematics and physics seminar series is planned. In addition we present attractive tracks for the students to presumably yield future mathematicians with more insight to actual problems in theoretical physics and physicists with some knowledge in the fields of modern mathematics