Boîte à outils pour une thèse en combinatoire Room: Salle Maryam Mirzakhani

Marguerite Bin - From Cubes to Tilings and Chirotopes, from Hypersimplices to k-levels and k-sets Room: Salle Maryam Mirzakhani A tiling of a zonogon by rhombi is called coherent if it corresponds to the visible faces of a zonotope in R^3. The problem of deciding whether a tiling is coherent is known to be difficult (in particular, it is NP-hard and ETR-complete). If we restrict ourselves to partial information about the tiling, such as its k-level, does the problem remain difficult? By interpreting this information geometrically, we will provide some answers to this question.

Ludovic Schwob : From middle orders to Jurassian lattices Room: Salle Maryam Mirzakhani The weak and Bruhat orders are well-studied posets on Coxeter groups. In a recent paper, we introduced middle orders, which are distributive lattices between the weak and Bruhat orders, describing all middle orders on the symmetric group, and a generalization of these on Weyl groups called minuscule middle orders. In this talk, I will explain how Jurassian lattices can be constructed from minuscule middle orders. These lattices share a lot of properties with Cambrian lattices, such as being congruence-uniform and extremal, having size Catalan(W), or being the 1-skeleton of a regular polytope.