Hugo Parlier

Curves, surfaces and intersection

Closed curves on surfaces and their intersections have been studied at least since the work of Dehn who understood how to describe the set of isotopy classes of simple curves by looking at their intersection with a finite set of curves. Now what if you want to describe curves with self-intersections in a similar way? This talk will be on joint work with Binbin Xu about this question, and where we end up constructing and studying k-equivalent curves. These are distinct curves that intersect all curves with k self-intersections the same number of times.