Explore the mathematical framework of diffusion approximation as applied to stochastic systems that undergo resetting processes in this 58-minute research lecture from the Instituto de Física Interdisciplinar y Sistemas Complejos. Delve into the theoretical foundations of how diffusion processes behave when subjected to periodic or random resets to initial conditions, examining the mathematical tools and approximation methods used to analyze such systems. Learn about the key principles governing diffusion with resetting, including the derivation of effective equations, steady-state solutions, and the impact of resetting rates on system dynamics. Discover applications of these concepts in physics, biology, and other complex systems where resetting mechanisms play a crucial role in determining long-term behavior and transport properties.