Sofic groups were first introduced by Mikhail Gromov as a common generalizations of amenable groups and residually finite groups. In 2008, in a remarkable breakthrough, via modeling the dynamics of a measurable partition of probability space by means of partitions of a finite space, Lewis Bowen showed how to define entropy for measure-preserving actions of countable sofic groups. Later, using ideas in operator algebras, David Kerr and Hanfeng Li, developed a more general approach for both measure and topological sofic entropies and established the variational principle for this context.

In this talk, applying Kerr and Li's method, we will define the topological pressure for actions of sofic groups and establish the variational principle for topological pressure.