Emmy-Noether group on String Mathematics was established on 1st of September 2016. The group consists of 7 researchers and is lead by Dr. Murad Alim. We are interested in basic questions at the interface of Mathematics and Physics, especially in the areas of complex and algebraic geometry, for example: How do we distinguish different geometric objects and what are their properties? What are the basic building blocks of quantum field theories and what can we learn about them by studying simplified models, such as supersymmetric ones? What can we infer about properties of associated geometries by studying these models?
The interplay between Mathematics and Physics has allowed us to look at some important mathematical problems from a very different perspective in the recent years. The discovery of Mirror Symmetry for example has led to a breadth of new results in the area of (complex) algebraic geometry and studying solutions of the Yang-Mills equations on curved manifolds allowed us to prove important conjectures about the structure of vector bundles on Riemann surfaces. On the other hand topological and geometric properties of manifolds tell us a lot about the spectrum of associated quantum field theories and in some cases even allow us to find exact solutions.
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..
Would you like to know more. Read more about our Research in the Research section or contact us at murad.alim"AT"uni-hamburg.de.