This Friday at 3pm several Undergraduate Reseachers presented a project to faculty, Balasz Strenner and Dan Margalit, in the Skiles building.

The project which was organized by the SoM faculty members, was about curves on surfaces: One can encode a curve on a surface as a path connecting various points on a surface. Some paths are clearly not efficient: if we go from A to B, then B to C, we could have simply gone from A to C. On higher genus surfaces, paths can be inefficient in more complicated ways, but one can make a list of what the inefficient paths can look like and how they can be made more efficient.

The students designed a way to encode paths as a sequence of letters and numbers, and wrote a Python-implementation of the curve tightening process, which looks for inefficient subpaths of a path and replaces them with their efficient counterparts. This curve tightening problem is an ingredient of my Macaw project, which is an implementation of a quadratic time algorithm of Margalit, Yurttas and myself for the Nielsen-Thurston classification problem of mapping class groups of surfaces.