Linear dynamical systems are a continuous subclass of reinforcement learning models that are widely used in robotics, finance, engineering, and meteorology. Classical control, since the works of Kalman, has focused on dynamics with Gaussian i.i.d. noise, quadratic loss functions and, in terms of provably efficient algorithms, known systems and observed state.
The stacky approach was originated by Bhatt and Lurie. (But the possible mistakes in my talk are mine.)
Let X be a scheme over F_p. Many years ago Grothendieck and Berthelot defined the notion of crystal on X; moreover, they defined the notion of crystalline cohomology of a crystal.