Abstract:

Calabi-Yau manifolds have many "hidden symmetries", which are autoequivalences that can not be generated by the standard ones like automorphisms, tensoring line bundles, and shiftings. By studying categorical entropy introduced by Dimitrov-Haiden-Katzarkov-Kontsevich, we show that the dynamical systems formed by the hidden symmetries and the actual symmetries have different behaviours. We will also explain the motivation coming from mirror symmetry of Calabi-Yau manifolds.