The main lectures were given by Guo-Niu Han (Strasbourg) and Igor Pak (Los Angeles). Guo-Niu Han reported on his "Recent Work on Hankel Determinants", showing us techniques for proving non-vanishing and/or periodicity of Hankel determinants which arise from the study of irrationality measures in number theory. Igor Pak on the other hand, in his series of lectures "New Foundations of Combinatorial Theory", presented us three beautiful selections from recent work of his, covering a wide variety of topics ranging from the use of tilings to generate integer sequences, partitions, Kronecker coefficients, up to counting integer points in polytopes, including of course his love, bijections, and he interspersed this with excursions of more "philosophical" nature, where he set out his view of the key words in the titles of his three lectures.
The contributed talks (see the detailed list below) covered also various topics, including the combinatorics of Coxeter groups, Kazhdan-Lusztig polynomials, Jack polynomials, Kostka numbers, partitions, and related polytopes, Kronecker coefficients, Schubert calculus, parking functions, permutations, and some conjectures by Atiyah in "elementary" geometry, which do not seem so "easy" to prove after all ...
Although weather forecast was not very promising, it turned out to be perfect for taking swims in the lake or hikes in the neighbourhood during the lunch breaks (with showers occurring only during the night and during lectures). In summary, this was another very pleasant Séminaire, with a lively exchange of ideas and fruitful discussions. It deserves special mention that this session of the Séminaire saw a record participation from the Lotharingian division in the Far East, with 5 participants from Japan.
Mathilde BOUVEL: A general theory of Wilf-equivalence for Catalan structures
Laura COLMENAREJO: Stability of plethysm coefficients
Angela CARNEVALE: A proof of two conjectures by B. Klopsch, A. Stasinski and C. Voll
Valentin FÉRAY: Shifted Jack polynomials and multirectangular coordinates
Antonio GUEDES DE OLIVEIRA: The braid and the Shi arrangements and the Pak-Stanley labelling
Masao ISHIKAWA: Selberg integrals and evaluations of Pfaffians
Hiroshi NARUSE: Schubert calculus and hook formula
Soichi OKADA: Pfaffian formulae and their applications to symmetric function identities
Mathias PÉTRÉOLLE: A Nekrasov-Okounkov formula in type C
Vivien RIPOLL: Coxeter elements in well-generated reflection groups
Paolo SENTINELLI: Complements of Coxeter group quotients
Dragutin SVRTAN: A proof of all three Euclidian four-point Atiyah-Sutcliffe conjectures