**Topics on flip graphs**

*(Jean Cardinal)*

A flip in a triangulation is a simple local operation involving neighboring
pairs of triangles, and consisting in exchanging the two diagonals of the
quadrilateral that they form. Such operations define so-called flip graphs on
sets of triangulations: every vertex of the graph is a triangulation, and two
vertices are adjacent whenever the triangulations differ by a single flip. For
triangulations of convex polygons, flip graphs are skeletons of associahedra, a
well-known family of polytopes. Associahedra also have applications to the
theory of binary search trees.

We will introduce such flip graphs and some of their generalizations, as well
as a number of important open questions, both on the combinatorial and
computational aspects. In particular, we plan to discuss flip graphs on
rectangulations, on tubings in graphs, and on regular triangulations of point
sets. These all have in common to be skeletons of polytopes.