Mathematics is a key technology for scientific and economic progress. New discoveries in mathematics are not only interesting in themselves, but they often lead to unexpected breakthroughs in other sciences as well.
We will tackle fundamentally important mathematical problems, viewing mathematics as an organic whole with countless interactions. Our research is unified by three major approaches: focusing on the underlying structure of a given problem, taking the geometric viewpoint and studying the relevant dynamics of group or semigroup actions. The theories which we will build will not only solve the problems under consideration but also many others of a similar nature; these theories will also raise exciting new questions.