On entropy of autoequivalences of smooth projective varieties

Entropy for endofunctors of triangulated categories is defined by Dmitrov–Haiden–Katzarkov–Kontsevich. Based on the joint work with Kohei Kikuta, the categorical entropy of an surjective endomorphism of a complex smooth projective variety is shown to be equal to its topological entropy, which is done by DHKK under a certain technical condition.
It is natural to expect a generalization of the fundamental theorem by Gromov–Yomdin: the entropy of an autoequivalence of a complex smooth projective variety should be given by the logarithm of the spectral radius of the induced automorphism of the numerical Grothendieck group. This conjecture holds for elliptic curves (Kikuta's result) and if the canonical or anti-canonical sheaf is ample.