Klassische Kombinatorik und Anwendungen

Christian Krattenthaler`s research focuses on problems in enumerative combinatorics, especially those which surface in other areas of mathematics, such as algebra, algebraic geometry or number theory, and in other scientific disciplines such as information science or statistical physics. Indeed, structural questions regarding reflection groups and classical groups, geometric questions, the combinatorial analysis of lattice models in statistical physics, and even Diophantine problems in analytical number theory raise questions which boil down to the enumeration of combinatorial objects. Christian Krattenthaler`s team has developed powerful methods, especially with regard to lattice path combinatorics and mathematical manipulation, and thus generated solutions to a number of difficult problems. Krattenthaler`s goal is to refine these methods and to develop new techniques in order to tackle new questions which have arisen. As this work is generally closely associated with the use of computers, the research will also (as in the past) give rise to computer programmes capable of solving those problems or facilitating the solution process.

The main goal of this project was to develop combinatorial methods, and apply them in various areas not only within mathematics. The applications included problems of exact and asymptotic enumeration, with applications to problems of statistical physics, structural investigations in geometric combinatorics, problems of number theory, of commutative algebra, and even of differential geometry. An important aspect of this project was to establish Vienna as a centre of combinatorics at an international level.