Applications of canonical relations in generic differential geometry

Conflict sets are loci of intersecting wavefronts emanating from $l$ different surfaces. We show that generically conflict sets are Legendrian: locally they admit the structure of wavefronts. Simple stable singularities for this problem in ${\mathbb{R}}^n$ occur when $0\le n-l\le 4$. Other related sets, such as kite curves and centre sets are also defined and discussed. Throughout canonical relations are used as an essential tool to carry out several of these geometrical constructions.