In the Emmy Noether group on String Mathematics, we are trying to understand the intricate interplay between the properties of quantum field theories and associated geometries , often making contact with stringy origin of the former. The goal of the overlying program is to understand the building blocks of quantum field theories by studying supersymmetric models and to investigate the geometry underlying the BPS states. Further, we would like to find a geometric interpretation of the count of these BPS states, by studying their moduli spaces. The topic is closely related to many recent, exciting developments in Mathematics, such as Mirror Symmetry, Hitchin Systems, Modular forms, etc..