**Title:** Multiple phase transitions on compact symbolic systems

**Speaker:** Tamara Kucherenko – City College of New York

**Abstract: **A first-order phase transition refers to a loss of differentiability of the pressure function with respect to a parameter regarded as the inverse temperature. Such non-differentiability necessarily implies coexistence of several equilibrium states, although the converse is not true. In the case of H\”older continuous potentials on transitive SFTs the pressure is real analytic and there are no phase transitions. Therefore, in order to allow the possibility of phase transitions one needs to consider potentials that are merely continuous. Note that the convexity of the pressure implies that a continuous potential has at most countably many phase transitions. We show that the case of infinitely many phase transitions can indeed be realized. In this talk we present a method to explicitly construct a continuous potential on a full shift with an infinite number of first order phase transitions occurring at any increasing sequence of predetermined points. This is based on joint work with Anthony Quas and Christian Wolf.