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Project Area A: Many-Body Phenomena

Project Area B: Semiclassical Asymptotics

Project Area C: Effective Single-Particle Systems beyond Wigner Dyson

Project Area D: Symmetry Classes and Symmetric Spaces

Project Area D: Symmetry Classes and Symmetric Spaces

D2

Developing a Riemannian/ analytic theory for symmetric supermanifolds
A. Alldridge, M Köln, T. Guhr, TP Duisburg-Essen, 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 large-N universality for ratios of random characteristic polynomials, the symmetry classification of topological insulators with and without interactions, and the connection between the Efetov-Wegner 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.
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