Combinatorial analysis of tableaux, plane partitions, rhombus tilings, alternating sign matrices

This project focusses on classical objects in combinatorial analysis: tableaux, plane partitions, rhombus tilings, alternating sign matrices. These objects are not only intimately related to each other (this is partially conjectural; it is one of the aims of the project to resolve these conjectures), they also link combinatorics to other axeas of mathematics, in particular representation theory of classical Lie groups and Lie algebras, and to statistical physics. The ultimate goal of this project is to improve significantly the understanding of these ubiquitous objects. This is going to be achieved by solving a number of open problems on the enumeration and on the structure of, and on the relation between these objects. It is also planned to apply the gathered knowledge and techniques to solve related problems in representation theory and number theory.