The Research Training Network ``Algebraic Combinatorics in Europe"
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)
- new bijections between maps and trees with interesting applications
to the Ising and the hard particle model on maps.
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