Related papers: Stringy Geometry and Topology of Orbifolds
This is a review. Comments are welcome. The observation that the structure of string theory is rich enough to include the standard model in rough outline is an old one, starting with the early constructions of free field constructions,…
We study cocycle properties of vertex operators and present an operator representation of cocycle operators, which are attached to vertex operators to ensure the duality of amplitudes. It is shown that this analysis makes it possible to…
These notes are devoted to the intriguing and still largely unexplored links between String Theory and Higher Spins, the types of excitations that lie behind its most cherished properties. A closer look at higher-spin fields provides some…
Possibilities for using geometry and topology to analyze statistical problems in biology raise a host of novel questions in geometry, probability, algebra, and combinatorics that demonstrate the power of biology to influence the future of…
An analysis of a special class of type II string theory compactifications is presented. We focus on recent work in one particular orientifold background of intersecting brane models and the resulting four dimensional gauge group and matter…
We describe a topological string theory which reproduces many aspects of the 1/N expansion of SU(N) Yang-Mills theory in two spacetime dimensions in the zero coupling (A=0) limit. The string theory is a modified version of topological…
This is a survey of the theory of real trees and their applications.
We introduce an orbifold induction procedure which provides a systematic construction of cyclic orbifolds, including their twisted sectors. The procedure gives counterparts in the orbifold theory of all the current-algebraic constructions…
Dynamics of a free point particle on a multi world-line is presented and shown to reduce to that of a bosonic string theory at the appropriate limit. Other higher dimensional extended objects are argued to appear at other regions of the…
String structures have played an important role in algebraic topology, via elliptic genera and elliptic cohomology, in differential geometry, via the study of higher geometric structures, and in physics, via partition functions. We extend…
This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory. The geometry of the arc space of an algebraic variety yields several new geometric invariants and brings new light to some classical…
Survey article on the geometry of spherical varieties. Invited survey for Transformation Groups.
In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.
I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical…
In this thesis we discuss some topics about topology and superstring backgrounds with D-branes. We start with a mathematical review about generalized homology and cohomology theories and the Atiyah-Hirzebruch spectral sequence, in order to…
If the vacuum manifold of a field theory has the appropriate topological structure, the theory admits topological structures analogous to the D-branes of string theory, in which defects of one dimension terminate on other defects of higher…
This is a survey on coarse geometry with an emphasis on coarse homology theories.
After a review of some topics concerning the phenomenological applications of perturbative string theory, I discuss to what extent all of it is affected by the recent developements in string dualities.
We find a direct relation between quiver representation theory and open topological string theory on a class of toric Calabi-Yau manifolds without compact four-cycles, also referred to as strip geometries. We show that various quantities…
Four-dimensional Kerr-Schild geometry contains two stringy structures. The first one is the closed string formed by the Kerr singular ring, and the second one is an open complex string with was obtained in the complex structure of the…