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We study some of the novel properties of conformal field theories with noncompact target spaces as applied to string theory. Standard CFT results get corrected by boundary terms in the target space in a way consistent with the expected…
In this set of lectures I review recent developments in string theory emphasizing their non-perturbative aspects and their recently discovered duality symmetries. The goal of the lectures is to make the recent exciting developments in…
Two solutions of stringy gravity in three and four dimensions which admit interpretation as a black hole and a black string, respectively, are discussed. It is demonstrated that they are exact WZWN nonlinear sigma models to all orders in…
We study the state-space geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a new perspective of black hole vacuum fluctuations. For a given black hole entropy, we…
Talk given at ICM '98, Berlin, reviewing some of the recent developments in understanding of string theory for a mathematical audience (to appear in Documenta Mathematica).
These notes were written following lectures I had the pleasure of giving on this subject at Keio University, during November and December 2004. The first part is about new applications of Jordan algebras to the geometry of Hermitian…
String propagation is investigated in de Sitter and black hole backgrounds using both exact and approximative methods. The circular string evolution in de Sitter space is discussed in detail with respect to energy and pressure, mathematical…
These notes are for the author's lectures, "Integral Reduction and Applied Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in Beijing 2016. I introduce the applications of algebraic geometry methods on multi-loop…
This is a survey written for the Proceedings of the AMS Summer Institute in Algebraic Geometry held in Seattle in 2005. Topics discussed in the survey include the ample and the effective cone of the moduli space of curves, Kodaira…
We find new classes of {\it exact} string solutions in a variety of curved backgrounds. They include stationary and dynamical (open, closed, straight, finitely and infinitely long) strings as well as {\it multi-string} solutions, in terms…
Contents of Part 1: 1. Status of the Standard Model(P.H. Frampton), 2. Cosmological Constraints from MBA and Polarization (A. Melchiorri), 3. AdS/CFT Correspondence and Unification at About 4 TeV (P.H. Frampton), 4. New Solutions in String…
These notes are an expanded version of the author's lectures at the graduate workshop "Noncommutative Algebraic Geometry" at the Mathematical Sciences Research Institute in June 2012. The main topics discussed are Artin-Schelter regular…
Talk given at the conference "Visions in Mathematics toward the year 2000", August 1999, Tel-Aviv.
CONTENTS: 1 Introduction 2 Analytic Manifolds and Analytic Continuation of Metrics 3 Walker's Spacetimes and their Maximal Extension 4 Global Structure of de Sitter and Reissner-Nordstr\"om-de Sitter Cosmos 4.1 Special Cases 4.2 Collapsing…
Early in 2011 Sam Evens acting on behalf of the organizers of the summer school on quantization at Notre Dame asked me to give a short series of lectures on geometric quantization. These lectures were meant to prepare a group of graduate…
Teaching the general theory of relativity to high school or undergraduate students must be based on an approach that is conceptual rather than mathematical. In this paper we present such an approach that requires no more than elementary…
We classify and construct supersymmetric solutions of D=3, N=2 gauged supergravity extended with a Fayet-Iliopoulos term, and null and timelike warped AdS spacetimes are among them. From the first one, it is possible to obtain a…
We study an exact model of string theory propagating in a space-time containing regions with closed time-like curves (CTCs) separated from a finite cosmological region bounded by a Big Bang and a Big Crunch. The model is an non-trivial…
We report on joint work, past and in progress, with K.Fredenhagen and with J.E,Roberts, on the quantum structure of spacetime in the small which is dictated by the principles of Quantum Mechanics and of General Relativity; we comment on how…
Plenary talk at the conference, LATTICE 99, held in Pisa, Itay from June 29 to July 3, 1999.