Related papers: Is the Universe Uniquely Determined by Invariance …
A hierarchy of type universes is a rudimentary ingredient in the type theories of many proof assistants to prevent the logical inconsistency resulting from combining dependent functions and the type-in-type rule. In this work, we argue that…
A geometric interpretation of quantum self-interacting string field theory is given. Relations between various approaches to the second quantization of an interacting string are described in terms of the geometric quantization. An algorithm…
In quantum field theory, an orbifold is a way to obtain a new theory from an old one by gauging a finite global symmetry. This definition of orbifold does not make sense for quantum gravity theories, that admit (conjecturally) no global…
We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…
I present a summary of the recent progress made in field and string theory which has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be described in…
An overview is given of the way in which the unification program of particle physics has evolved into the proposal of superstring theory as a prime candidate for unifying quantum gravity with the other forces and particles of nature. A key…
We consider string theory in a time dependent orbifold with a null singularity. The singularity separates a contracting universe from an expanding universe, thus constituting a big crunch followed by a big bang. We quantize the theory both…
A powerful way to study groups is via their actions on suitable spaces. Classifying spaces for families of subgroups are a type of these spaces, obtained by imposing some strict conditions on the fixed-point sets. We show how in the…
This book provides an introduction to string field theory (SFT). String theory is usually formulated in the worldsheet formalism, which describes a single string (first-quantization). While this approach is intuitive and could be pushed far…
We establish a connection between knot theory and cluster algebras via representation theory. To every knot diagram (or link diagram), we associate a cluster algebra by constructing a quiver with potential. The rank of the cluster algebra…
At its very beginning, the universe is believed to have grown exponentially in size via the mechanism of inflation. The almost scale-invariant density perturbation spectrum predicted by inflation is strongly supported by cosmological…
String theory is a quantum theory that reproduces the results of General Relativity at long distances but is completely different at short distances. Mathematically, string theory is based on a very new -- and little understood -- framework…
Loop Quantum Gravity provides a natural truncation of the infinite degrees of freedom of gravity, obtained by studying the theory on a given finite graph. We review this procedure and we present the construction of the canonical theory on a…
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
In this talk we discuss the quantisation of a class of string cosmology models characterised by scale factor duality invariance. The amplitudes for the full set of classically allowed and forbidden transitions are computed by applying the…
It is hoped that these lectures will give a point of entry into that vast web of related ideas that go under the name "string theory". I start with a more or less qualitative introduction to gravity as a field theory and sketch how one…
We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their…
The doubled formulation of string theory, which is T-duality covariant and enlarges spacetime with extra coordinates conjugate to winding number, is reformulated and its geometric and topological features examined. It is used to formulate…
I review some of the recent progress in two-dimensional string theory, which is formulated as a sum over surfaces embedded in one dimension.
Quantification starts with sum and product rules that express combination and partition. These rules rest on elementary symmetries that have wide applicability, which explains why arithmetical adding up and splitting into proportions are…