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We discuss the possible applications of string theory for the construction of generalizations of the $SU(3)\times SU(2)\times U(1)$ standard model of strong and electroweak interactions. This includes an investigation of effective $d=4$…

We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces…

String theory is at the moment the only advanced approach to a unification of all interactions, including gravity. But, in spite of the more than thirty years of its existence, it does not make any empirically testable predictions, and it…

String-bit models are both an efficient way of organizing string perturbation theory, and a possible non-perturbative composite description of string theory. This is a summary of ideas and results of string-bit and superstring-bit models,…

This is a set of lectures given at the 99' Cargese Summer School: Particle Physics : Ideas and Recent Developments. They contain a pedestrian exposition of recent theoretical progress in non-perturbative field theory and string theory based…

We give an introduction to the statistical approach to studying vacua of string/M theory, and discuss recent results of Ashok and Douglas on counting supersymmetric flux vacua in type IIb Calabi-Yau compactification. To appear in the…

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).

Ever since its birth, up until its present development, the major role of string theory involves being the best candidate for the theory of quantum gravity and other species of interactions. In the present work, we would like to accomplish…

The string duality revolution calls into question virtually all of the working assumptions of string model builders. A number of difficult questions arise. I use fractional charge as an example of a criterion which one would hope is robust…

We study the computational complexity of the physical problem of finding vacua of string theory which agree with data, such as the cosmological constant, and show that such problems are typically NP hard. In particular, we prove that in the…

We explore the four dimensional Einstein-Maxwell landscape as a toy model in which we can formulate a sphere compactification stabilized by an electromagnetic field. Replacing the compactification sphere by J spheres, we obtain a simple…

Considered are superparticle and superstring models invariant under supersymmetry in a target superspace and local extended worldsheet supersymmetry the latter replacing the fermionic $\kappa$--symmetry of the conventional Green--Schwarz…

In these lectures we review how some of the recent developments in string theory are closely related to generic properties of supersymmetry. Lectures given at the Nato Advanced Study Institute on "Strings, Branes and Dualities", Cargese,…

These are the lecture notes for a short course in topological string theory that I gave at Uppsala University in the fall of 2004. The notes are aimed at PhD students who have studied quantum field theory and general relativity, and who…

These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.

The landscape of string/M theory is surveyed over a large class of type $IIB$ flux compactification vacua. We derive a simple formula for the average size of the gauge group rank on the landscape under assumptions that we clearly state. We…

The gauge symmetries that underlie string theory arise from inner automorphisms of the algebra of observables of the associated conformal field theory. In this way it is possible to study broken and unbroken symmetries on the same footing,…

In this semi-technical review we discuss string theory (and all that goes by that name) as a framework for a quantum theory of gravity. This is a new paradigm in theoretical physics that goes beyond relativistic quantum field theory. We…

One of the central problems of string-phenomenology is to find stable vacua in the four dimensional effective theories which result from compactification. We present an algorithmic method to find all of the vacua of any given…

These are lecture notes for two lectures delivered at the Les Houches workshop on Number Theory, Physics, and Geometry, March 2003. They review two examples of interesting interactions between number theory and string compactification, and…