250527 Aaron Gootjes-Dreesbach

Blowing up the diagonal of M^2 for a manifold M yields a configuration space that remembers the collision axis of collided configurations. Fulton and MacPherson famously generalized this construction to configurations of more than two points. As part of my thesis advised by Á. del Pino, we build configuration spaces for jets of maps in the same spirit, but adapted to the main structure on jet space: The Cartan distribution and the Lie filtration it generates. Higher jet orders necessitate the use of *weighted* blow-ups, which we tackle within the differential-geometric framework of *weightings* due to Loizides and Meinrenken. In this talk, I first want to intuitively illustrate this construction and then motivate why it is natural to consider when studying h-principles for differential constraints involving multiple points.