CATS is a series of conferences devoted to categories and stacks in algebraic geometry and algebraic topology. Derived algebraic geometry is the spearhead of this huge program that aims (among other things) at using homotopical methods to study geometric objects (such as various kinds of moduli spaces). It is a very active area that connects with several topics: symplectic geometry, enumerative invariants, categorification, higher categories, singularities, mathematical physics, etc.

CATS7 will be the occasion to celebrate Bertrand Toën‘s 50th birthday, and will serve as a closing conference for two projects: the ANR project CatAG (Categorification in Algebraic Geometry) and the ERC project DerSympApp (Derived Symplectic geometry and Applications). It will shed light on recent developments and will provide a state of the art of the subject.