Symmetries in Diffusion Equations

This lecture introduces the concept of symmetries in diffusion equations, focusing on equivariances and isotropies of the system and solutions. The instructor explains how symmetries are related to translation, reflection, and rotation, and demonstrates how symmetries can simplify the analysis of solutions. By examining the symmetries of the system and solutions, the lecture shows how certain properties of the solutions can be inferred without explicitly solving the equation. The importance of symmetries in understanding the behavior of diffusion equations is highlighted, emphasizing the role of symmetries in identifying integrated quantities and symmetric subspaces.