Overview

Knot theory is the branch of Low Dimensional Topology concerned with the study of the configuration of  circles  embedded in the three-dimensional space. The early years of this theory   were  primarily   driven  by its application in chemistry. More recently, the discovery of knotted DNA molecules by biologists brought intense attention to knot theory. Collaboration between cell biologists and knot theorists shows that the theory can be successfully used to build robust  mathematical models for the action of certain enzymes on circular DNA molecule.

A spatial graph is  an  embedding of an abstract graph into the three-dimensional space.  These embeddings are considered up to natural deformations. The theory of spatial graphs is  considered as a natural extension of knot theory. Therefore,  many of the techniques and problems   of knot theory have their counterparts in spatial graph theory. Addressing these kind of problems solicits techniques from a range of mathematical disciplines at the interface of algebra, analysis, geometry, modeling, and low-dimensional topology.

The workshop primarily addresses fundamental questions in knot theory and low dimensional topology in general.  It will bring together wide range of leading experts in the field    to discuss the state of the art in current research, both in terms of core fundamental problems and crossover to other areas, and explore exciting new directions. Research topics  to be discussed at  the workshop  include combinatorial knot theory,  link homologies, topological invariants of links and spatial graphs, in addition to    applications of knots  and spatial graphs in other fields of  science and mathematics.