New Techniques for the Resolution of Singularities of Vector Fields and Differential Operators

Explore advanced mathematical concepts in this graduate-level lecture on new techniques for resolving singularities in vector fields and differential operators. Delve into the importance of studying differential operators, their order, and localization. Examine the process of defining singular loci and reducing singularities, with a focus on the geometric environment theorem. Learn about convenient coordinate systems and direct sum decomposition through detailed explanations and examples. This 1-hour 44-minute talk by Daniel Cantergiani Panazzolo from Université de Haute Alsace is part of the Fields Institute's Graduate Course on Transseries and Asymptotic Analysis, offering valuable insights for researchers and advanced students in mathematics.

Introduction
Why study differential operators
Order of differential operators
Localisation of differential operators
General discussion
Defining the singular locus
Reduction of singularities
Geometric environment theorem
A convenient system of coordinates
Direct sum decomposition
Example