Explore advanced mathematical concepts in this 51-minute graduate-level lecture on new techniques for resolving singularities in vector fields and differential operators. Delve into topics such as adapted local charts, semidirect sum products, stable systems, and local resolution similarity. Learn about eliminating pitch points, transforming axes, and stabilizing faces. Presented by Daniel Cantergiani Panazzolo from Université de Haute Alsace as part of the Fields Institute's Graduate Course on Transseries and Asymptotic Analysis, this talk offers a deep dive into cutting-edge mathematical research.