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*

- Olga Azenhas (Coimbra)
- Sabine Beil (Wien)
- Adam Bohn (London)
- Petter Brändén (Stockholm)
- Matthew Chasse (Stockholm)
- Gérard Duchamp (Paris)
- Theresia Eisenkölbl (Lyon)
- Dominique Foata (Strasbourg)
- Ilse Fischer (Wien)
- Masao Ishikawa (+1) (Nishihara)
- Matthieu Josuat-Vergès (Marne-la-Vallée)
- Myrto Kallipoliti (+1) (Wien)
- Anisse Kasraoui (Wien)
- Christian Krattenthaler (Wien)
- Bodo Lass (Lyon)
- Madeleine Leander (Stockholm)
- Bernard Leclerc (Caen)
- Rémi Maurice (Marne-la-Vallée)
- Henri Mühle (Wien)
- Philippe Nadeau (Lyon)
- Hoang-Nghia Nguyen (Paris)
- Eric Nordenstam (Wien)
- Soichi Okada (Nagoya)
- Konrad Podloucky (Wien)
- Lukas Riegler (Wien)
- Christopher Schure (Hannover)
- Volker Strehl (+1) (Erlangen)
- Jean-Yves Thibon (Marne-la-Vallée)
- Marko Thiel (Wien)
- Leandro Vendramin (Marburg)
- Mirkó Visontai (Stockholm)