This volume contains the proceedings of the ICTS program Knot Theory and Its Applications (KTH-2013), held from December 10-20, 2013, at IISER Mohali, India. The meeting focused on the broad area of knot theory and its interaction with other disciplines of theoretical science. The program was divided into two parts. The first part was a week-long advanced school which consisted of minicourses. The second part was a discussion meeting that was meant to connect the school to the modern research areas. This volume consists of lecture notes on the topics of the advanced school, as well as surveys and research papers on current topics that connect the lecture notes with cutting-edge research in the broad area of knot theory.

Lecture Notes

Knot Theory

From Conway Notation to LinKnot

Surface-knots

An Introduction to Khovanov Homology

Knot Theory for Spatial Graphs Attached to a Surface

Knots and Graphs: Two Centuries of Interaction

Research Expositions

On the Welded Tube Map

On Representations of Braids as Automorphisms of Free Groups and

Corresponding Linear Representations

Ribbon Graphs and Temperley-Lieb Algebra

On Twisted Knots

Tunnel Numbers of Knots

The Warping Matrix of a Knot Diagram

On Arf Invariant and Trivializing Number

About the Authors

Krishnendu Gongopadhyay, Indian Institute of Science Education and Research, Mohali, Punjab, India.

Rama Mishra, Indian Institute of Science Education and Research, Pune, India.