The Research Training Network “Algebraic Combinatorics in Europe”

Abstract

I present four highlights from the scientific activities of the eight teams of the Research Training Network “Algebraic Combinatorics in Europe” in Bordeaux, Jerusalem, Linköping, Lyon, Marburg, Marne-la-Vallée, Roma, and Wien:

• the proof of the combinatorial invariance conjecture for Kazhdan–Lusztig polynomials in an important special case;
• the proof of the conjectures on the random assignment problem;
• important progress on the Neggers–Stanley Conjecture on posets and the Charney–Davis conjecture on (certain) simplicial complexes;
• new bijections between maps and trees with interesting applications to the Ising and the hard particle model on maps.