Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of the various questions raised.

Introduction.- Black Holes and First Order Flows in Supergravity.- Representations of Super Lie Groups: Some Remarks.- On Chiral Quantum Superspaces.- On the Construction of Chevalley Supergroup.- Indecomposable Finite-dimensional Representations of a Class o f Lie algebras and Lie Superalgebras.- On the Geometry of Super Riemann Surfaces.- Charge Orbits and Moduli Spaces of Black Hole Attractors.- Maximal Supersymmetry.- Lie Supergroups, Unitary Representations, and Invariant Cones.- Geometry of Dual Pairs of Complex Supercurves.- On the Superdimension of an Irreducible Representation.

Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. Since then its mathematical structure has been recognized as that of a new development in geometry, and mathematicians have busied themselves with exploring this aspect. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of the various questions raised.

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