
Project Area D: Symmetry Classes and Symmetric Spaces


D2 
Developing a Riemannian/ analytic theory for symmetric supermanifolds 
A. Alldridge, M Köln, T. Guhr, TP DuisburgEssen, P. Heinzner, M Bochum, T. Wurzbacher, M Bochum 

Methods based on supersymmetry  an operation relating fermions with bosons  have become an important tool for handling random matrices and disordered systems. Our goal is to provide a solid mathematical foundation to existing mesoscopic physics technology and to prepare the way for novel types of application. 




D4 
Howe pairs and Fock representations, and conformal fields 
A. Huckleberry, M Bochum, A. Püttmann, M Bochum, T. Quella, TP Köln, J. Winkelmann, M Bochum, M. Zirnbauer, TP Köln 

The basic mathematical setting of this project is that of a Fock space carrying a pair of commuting group actions, one given by the Hamiltonians and the other by the symmetries of the physical system. Prototypical examples are Howe dual pairs acting on a Fock space for fermions or bosons or a tensor product for both particle types. In this general setting we investigate the question of largeN universality for ratios of random characteristic polynomials, the symmetry classification of topological insulators with and without interactions, and the connection between the EfetovWegner supersymmetry method and free probability theory. We also study superspace sigma models with conformal symmetry and some foundational issues of relevance in the complex analytic theory of symmetric supermanifolds. 



