A surprising discovery of 20th century mathematics is that many deterministic systems exhibit random behavior. One of an early examples of chaotic system was Lorenz equation used by meteorologist Edward Lorenz as a simplified model of atmospheric convection. One of the most common mechanisms of stochasticity is the Smale horseshoe appearing near a homoclinic intersection. The Lorentz attractor and Smale horseshoe are typical examples of fractal invariant sets for dynamical systems. Fractal objects are ubiquitous in dynamics, including invariant sets, invariant measures, invariant foliations et cetera. Thermodynamical formalism is a powerful tool for studying dimensions of fractal objects. It originated in statistical mechanics, but currently it has applications to many area of mathematics including spectral theory, hyperbolic geometry and probability theory. The goal of this conference is to bring together experts studying fractal objects in dynamics in order to review recent progress in the field and catalyze further research.