UNIVERSAL TEICHMULLER SPACE IN GEOMETRY AND PHYSICS

Lipman Bers' universal Teichmuller space, classically denoted by T(1), plays a significant role in Teichmuller theory, because all the Teich muller spaces T(G) of Fuchsian groups G can be embedded into it as com plex submanifolds. Recently, T(1) has also become an object of intensi ve study in physics, because it is a promising geometric environment f or a non-perturbative version of bosonic string theory. We provide a n on-technical survey of what is currently known about the geometry of T (1) and what is conjectured about its physical meaning. Our bibliograp hy should be rather comprehensive, but we apologize for any unjustifie d omissions.