Explore a 32-minute lecture on "Singularities and diffeomorphism" presented by Tobias Colding from the Massachusetts Institute of Technology at IPAM's Calculus of Variations in Probability and Geometry Workshop. Delve into the main problem, special cases, and richer flow concepts before examining singularities and their classification. Follow the theorem's extension, proof, and improvement, covering topics such as propagation, quadratic rigidity, and polynomials. Investigate the gate problem, infinite dimension, and linearization before concluding with a comprehensive summary. Gain insights into advanced mathematical concepts and their applications in probability and geometry.