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Two dimensional classical string theory is solved in any curved spacetime. The complete spacetime required to describe the classical string motions turns out to be larger than the global space required by complete particle geodesics. The…
We explore the possibility of string theories in only four spacetime dimensions without any additional compactified dimensions. We show that, provided the theory is defined in curved spacetime that has a cosmological interpration, it is…
To appear in Encyclopedia of Mathematical Physics, J.-P. Fran\c{c}oise, G. Naber and T.S. Tsou, eds., Elsevier, 2006. The article surveys the modern developments of noncommutative geometry in string theory.
Open and Closed super-string field theories are constructed in an event-symmetric target space. The partition functions of Statistical and Quantum models are constructed in terms of invariants defined on Lie-algebra representations. An…
Lectures presented at the Spring School, Trieste, Italy 1993.
We illustrate the various ways in which the algebraic framework of noncommutative geometry naturally captures the short-distance spacetime properties of string theory. We describe the noncommutative spacetime constructed from a vertex…
A brief overview of strings propagating on noncompact coset spaces G/H is presented in terms of WZW models. The role played by isometries in the existence of target space duality and by fixed points of the gauge transformations in the…
Lecture given at ``Raychaudhuri session," ICGC-95 conference, Pune (India), December 1995. Contents: I. Introduction II. (2+1)-Dimensional Initial Values in Stereographic Projection A. The single, non-rotating black hole B. Non-rotating…
In these notes we review the role played by the quantum mechanics and sigma models of symmetric product spaces in the light-cone quantization of quantum field theories, string theory and matrix theory. Lectures given at the Institute for…
Active feedback between geometry and physics is woven throughout the study of Nature at its fundamental level, and is of key importance in string theory. Methods of complex algebraic geometry in particular have brought about an unrivaled…
These notes introduce basic aspects of black hole thermodynamics. I review the classical laws of black hole mechanics, give a brief introduction to the essential concepts of quantum field theory in curved spacetime, and derive the Unruh and…
These are the author's lectures at the 1992 Les Houches Summer School, "Gravitation and Quantizations". They develop a generalized sum-over-histories quantum mechanics for quantum cosmology that does not require either a preferred notion of…
This monograph provides a largely self--contained and broadly accessible exposition of two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according…
The complete set of solutions of two dimensional classical string theory are constructed for any curved spacetime. They describe folded strings moving in curved spacetime. Surprizing stringy behavior becomes evident at singularities such as…
This is a pedagogic account of some of the global properties of Anti-de-Sitter spacetime with a view to their application to the AdS/CFT correspondence. Particular care is taken over the distinction between Anti-de-Sitter and it's covering…
These are notes from a lecture course on symmetric spaces by the second author given at the University of Pittsburgh in the fall of 2010.
These are expanded notes from a four lecture mini-course given by the author at the Spring School on Non-archimedean geometry and Eigenvarieties, held at the University of Heidelberg in March 2023. The course discusses coherent sheaves,…
This are the notes of a course, given by the first author for the Graduiertenkollegs (=graduate students) at the Ruhr-University Bochum, in December 1997. These lectures pursued two main tasks: FIRST - to give a systematic and…
In this thesis we study string compactifications on manifolds equipped with a $G$-structure, placing a special emphasis on the interplay between geometry and physics. We follow two complementary approaches. In the first part of the thesis…
A brief review of some of the central ideas, terminology and techniques of the technology of orientifolds and D-branes is presented. Some applications are reviewed, including the construction of dual solitonic strings in the context of…