The focus of this project is the study of several families of combinatorial objects including plane partitions,
rhombus tilings, vicious walkers and alternating sign matrices. The enumeration of these objects often leads to the
problem of evaluation of families of determinants or Pfaffians with polynomial entries.
The aim of this project is to improve the understanding of these objects and of the connections between them by
solving a number of open problems coming from combinatorics and statistical mechanics.
In doing so, it is planned to refine and further develop the methods for evaluating determinants and Pfaffians of
this kind exactly and asymptotically.