On the Rouquier dimension of wrapped Fukaya categories and a conjecture of Orlov

We study the Rouquier dimension of wrapped Fukaya categories Liouville manifolds and pairs, apply this invariant to various problems in algebraic symplectic geometry. On algebro-geometric side, we introduce a new method based on flexibility mirror symmetry bound derived coherent sheaves certain complex varieties stacks. These bounds are sharp at most $3$ . As an application, resolve well-known conjecture Orlov for classes examples (e.g. toric -folds, log Calabi–Yau surfaces). also discuss applications non-commutative motives partially categories. quantitative questions including following. (1) Given Weinstein manifold, what is minimal number intersection points between skeleton its image under generic compactly supported Hamiltonian diffeomorphism? (2) What critical Lefschetz fibration manifold with fibers? give lower these quantities which best authors’ knowledge first go beyond basic flexible/rigid dichotomy.