This time we had the pleasure to be introduced to the elegant theory of stable functions by Petter Brändén who gave us a series of lectures on "Zeros of Multivariate Polynomials in Combinatorics". The second series of lectures, "Cluster Algebras and Lie Theory", was given by Bernard Leclerc, who presented us a very motivated introduction to Fomin and Zelevinsky's cluster algebras, followed by a survey of recent results of his and co-authors, lending deep insight into the structure of cluster algebras related to Lie theory, including a glimpse of categorification.
Several of the contributed talks (see the detailed list below) connected to the main lectures in that they addressed combinatorial questions related to (finite) Coxeter groups or zeroes of combinatorial polynomials. Other talks concerned combinatorial Hopf algebras, orthogonal polynomials, and problems of enumeration.
Weather stuck precisely to the forecast, which meant that the participants could enjoy swimming in the lake on Monday and Tuesday, and typical (rainy) Salzkammergut weather on Wednesday ... In summary, this was another very enjoyable Séminaire, with very interesting, productive discussions.
Adam BOHN: On the question on which algebraic integers are chromatic roots
Gérard DUCHAMP: Fuchsian-type multipliers and shuffle algebras
Matthieu JOSUAT-VERGÈS: A Coxeter theoretic interpretation of Euler numbers
Myrto KALLIPOLITI: Integer partition models for extended Catalan arrangements and generalized cluster complexes
Anisse KASRAOUI: Difference equations and linearization of a product of orthogonal polynomials
Bodo LASS: Mehler formulae for multivariate matching polynomials of graphs
Henri MÜHLE: The Cambrian lattices are EL-shellable
Philippe NADEAU: Dual braid monoids and Koszulity
Nguyen HOANG-NGHIA: A word Hopf algebra based on the selection/quotient principle
Eric NORDENSTAM: Tilings of half a hexagon
Leandro VENDRAMIN: Nichols algebras
Mirkó VISONTAI: Roots of generalized Eulerian polynomials arising from inversion sequences