At the origin of these developments stand, on the combinatorics side, the conjectures on the enumeration of symmetry classes of plane partitions and alternating sign matrices (most of them proved now) and, on the physics side, the conjectures on combinatorial interpretations of the coordinates of the groundstate vectors of certain Hamiltonians in the dense O(1) loop model by Batchelor, de Gier, Nienhuis, Razumov, and Stroganov (most of them still open). The fact that, to this date, many mysterious connections that one observes empirically in this research area have no intrinsic explanation contributes to the fascination that it exerts, with almost any new result posing more new open questions than it answers.
The lectures of this seminar will demonstrate how combinatorics and physics interact to produce techniques to approach these problems, it will show how this area relates to other areas of mathematics and physics (such as classical group characters, orbital varieties, integrable models, quantum Knizhnik-Zamolodchikov equations) and they will report on the recent progress which has been made.
- full name and address, including e-mail address
- present position, university
- name of supervisor of Ph.D. thesis
- a short summary of previous work and interest
should be sent as hard copy or by e-mail (.ps or .pdf file) to:
Prof. Dr. Gert-Martin Greuel
Universität Kaiserslautern
Fachbereich Mathematik
Erwin Schrödingerstr.
67663 Kaiserslautern, Germany
.