Asymptotic limits of SCFTs and their relation to corresponding geometric structures, combining techniques from SCFT, noncommutative geometry, and algebraic geometry

该项目旨在将先前开发的共形场论的极限过程的概念扩展到超对称环境。在简并的超共形场理论中，人们期望借助于非对易几何的技巧，得到包括度规、伸缩子、复结构以及适当的狄拉克算符在内的几何解释。所得到的退化几何应与在镜像对称的上下文中扮演重要角色的那些Gromov-Hausdorff类型极限进行比较，并优选地加以识别，例如，在Siebert及其合作者的工作中，该工作已经在SPP 1154的保护伞下获得资助。该项目还包括对一类重要例子的应用，这些例子有望在奇点理论中产生有趣的见解。总而言之，对整个结构的完整几何理解是在SCFT的限制下产生的。

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 e.g. in the work of Siebert and collaborators, which is already funded under the umbrella of the SPP 1154. 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 SCFTs is aimed for.