Abstract: 

Ergodic optimization investigates the properties of invariant measures that maximize (or minimize) the space average of a continuous potential function. Typical Periodic Optimization (TPO) is the phenomenon where, in spaces of regular functions, a generic function has a unique maximizing measure, and this measure is supported on a periodic orbit. Following Contreras' resolution of the TPO Conjecture for expanding open mappings, this talk will focus on extensions of this result to: - Symbolic systems, including all sofic shifts, by identifying the Markov boundary as the only possible source of failure of TPO (joint work with Wen Huang, Leiye Xu & Yiwei Zhang). - The problem of Joint TPO, where both the dynamical system and the potential are varied in suitable spaces, and the maximizing measure may again be generically periodic (joint work with Zelai Hao, Yinying Huang & Zhiqiang Li).

Zoom Meeting ID: 832 0847 3832