##### Department of Mathematics,

University of California San Diego

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### Math 211 - Group Actions Seminar

## Tamara Kucherenko

#### City College of New York

## Flexibility of the Pressure Function

##### Abstract:

Our settings are one-dimensional compact symbolic systems. We discuss the flexibility of the pressure function of a continuous potential (observable) with respect to a parameter regarded as the inverse temperature. The points of non-differentiability of this function are of particular interest in statistical physics since they correspond to qualitative changes of the characteristics of a dynamical system referred to as phase transitions. It is well known that the pressure function is convex, Lipschitz, and has an asymptote at infinity. We show that these are the only restrictions. We present a method to explicitly construct a continuous potential whose pressure function coincides with any prescribed convex Lipschitz asymptotically linear function starting at a given positive value of the parameter. \\ \\ This is based on joint work with Anthony Quas.

Host: Brandon Seward

### February 9, 2021

### 9:00 AM

### Zoom ID 967 4109 3409 (email Nattalie Tamam or Brandon Seward for the password)

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