Related papers: Notes on topological strings and knot contact homo…
This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects.
These lecture notes review the topological string theory and its applications to mathematics and physics. They expand on material presented at the Takagi Lectures of the Mathematical Society of Japan on 21 June 2008 at Department of…
This paper is an exposition of the new subject of String Topology. We present an introduction to this exciting new area, as well as a survey of some of the latest developments, and our views about future directions of research. We begin…
Knot contact homology studies symplectic and contact geometric properties of conormals of knots in 3-manifolds using holomorphic curve techniques. It has connections to both mathematical and physical theories. On the mathematical side, we…
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…
We provide various formulations of knot homology that are predicted by string dualities. In addition, we also explain the rich algebraic structure of knot homology which can be understood in terms of geometric representation theory in these…
We review the relation between Chern-Simons gauge theory and topological string theory on noncompact Calabi-Yau spaces. This relation has made possible to give an exact solution of topological string theory on these spaces to all orders in…
We conjecture a relation between the sl(N) knot homology, recently introduced by Khovanov and Rozansky, and the spectrum of BPS states captured by open topological strings. This conjecture leads to new regularities among the sl(N) knot…
In these lectures I review recent attempts to apply string theory to cosmology, including string cosmology and various models of brane cosmology. In addition, the review includes an introduction to inflation as well as a discussion of…
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…
We study the connection between topological strings and contact homology recently proposed in the context of knot invariants. In particular, we establish the proposed relation between the Gromov-Witten disk amplitudes of a Lagrangian…
We give an introductory review of topological strings and their application to various aspects of superstrings and supersymmetric gauge theories. This review includes developing the necessary mathematical background for topological strings,…
I briefly review several important formal theory developments in quantum field theory and string theory that were reported at ICHEP conferences in past decades, and explain how they underlie a new research area referred to as physical or…
Knot theory provides a powerful tool for the understanding of topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in the quantum spin system. Exactly solvable models with…
In these lecture notes we discuss a body of work in which Morse theory is used to construct various homology and cohomology operations. In the classical setting of algebraic topology this is done by constructing a moduli space of graph…
The conormal Lagrangian $L_K$ of a knot $K$ in $\mathbb{R}^3$ is the submanifold of the cotangent bundle $T^* \mathbb{R}^3$ consisting of covectors along $K$ that annihilate tangent vectors to $K$. By intersecting with the unit cotangent…
This review summarizes the recent developments in topological string theory from the author's perspective, mostly focused on aspects of research in which the author is involved. After a brief overview of the theory, we discuss two aspects…
The purpose of this note is to provide a short invitation to the universal algebraic approach to topological string theory. In the first section we make an attempt to explain the origin of this approach and how it fits into the bigger…
This is an expository paper discussing various versions of Khovanov homology theories, interrelations between them, their properties, and their applications to other areas of knot theory and low-dimensional topology.
In this thesis we investigate topological aspects and arithmetic structures in quantum field theory and string theory. Particular focus is put on consistent truncations of supergravity and compactifications of F-theory.