Explore the intriguing phenomenon of spontaneous stochasticity in multi-scale dynamical systems through this comprehensive mathematics colloquium talk. Delve into the fascinating world where deterministic Cauchy problems are solved by stochastic Markov processes, with a focus on applications in turbulence models. Discover how these stochastic solutions are formalized using attractors of renormalization-group operators. Join speaker Alexei Mailybaev from IMPA, Rio de Janeiro, as he presents joint work with Artem Raibekas (UFF, Brazil), offering a captivating introduction to this complex topic in the field of mathematics and dynamical systems.