There are several features that could be added to the existing application: capability to evolve and tile higher genus surfaces, a mechanism to prevent the evolution of concave, non-tileable polygons that appear to the program to be legitimate solutions yet are obviously wrong; a means to identify which sides are paired; a counter to display the Teichmüller distance one has moved from the initial polygon. Also, David and Paul believe that we will be able to integrate this depiction of Riemann surfaces with the other tools for examining them worked on this summer. as I mentioned in the previous section, it would be useful to actually see the surfaces as embeddings in three-dimensional space changing as the geometry upon them was changed (i.e. the tiling was changed), or to have a better idea of how the different Riemann surfaces are actually related to different algebraic equations in two complex variables. The other projects that were done this summer relating to the study of Riemann surfaces, which might be one day integrated with Teichmüller Navigator were those of Sang Chin, Hiren Parekh, and Juliette Benitez. Their project reports may be referenced for more discussion of Riemann surfaces.