Shifting numbers in triangulated categories

Abstract: One can consider endofunctors of triangulated categories as dynamical systems, and study their long term behaviors under large iterations. There are (at least) three natural invariants that one can associate to endofunctors from the dynamical perspective: categorical entropy, and upper/lower shifting numbers. We will recall some background on categorical dynamical systems and categorical entropy, and introduce the notion of shifting numbers, which measure the asymptotic amount by which an endofunctor of a triangulated category translates inside the category. The shifting numbers are analogous to Poincare translation numbers. We additionally establish that in some examples the shifting numbers provide a quasimorphism on the group of autoequivalences. Joint work with Simion Filip.

mathematical physicsalgebraic geometrysymplectic geometry

Audience: researchers in the topic

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