Hopkins, Michael JYang, Lucy2023-06-0220232023-05-162023-05Yang, Lucy. 2023. Categorical dynamics on stable module categories. Doctoral dissertation, Harvard University Graduate School of Arts and Sciences.30492015https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37375794Let A be a finite connected graded cocommutative Hopf algebra over a field k. There is an endofunctor tw on the stable module category StMod A of A which twists the grading by 1. We show the categorical entropy of tw is zero. We provide a lower bound for the categorical polynomial entropy of tw in terms of the Krull dimension of the cohomology of A, and an upper bound in terms of the existence of finite resolutions of A-modules of a particular form. We employ these tools to compute the categorical polynomial entropy of the twist functor for examples of finite graded Hopf algebras over F 2 .application/pdfenMathematicsThesis or Dissertation2023-06-020000-0001-5414-1106