Towards the boundary of moduli spaces of superconformal field theories

The project aims to extend the previously developed notion of limiting processes for conformal field theories to the supersymmetric setting. It is expected that by means of techniques from noncommutative geometry in the resulting degenerate superconformal field theories, geometric interpretations can be obtained which include a metric, a dilaton, and a complex structure along with appropriate Dirac operators. The resulting degenerate geometries shall be compared and preferably identified with those Gromov-Hausdorff type limits that play a vital role in the context of mirror symmetry. The project also includes applications to an important class of examples which is expected to yield interesting insights in singularity theory. Altogether a complete geometric understanding for the entire structure that arises in limits of superconformal field theories is aimed for.