# Course Identification

## Lecturers and Teaching Assistants

## Course Schedule and Location

## Field of Study, Course Type and Credit Points

## Comments

## Prerequisites

## Restrictions

## Language of Instruction

## Attendance and participation

## Grade Type

## Grade Breakdown (in %)

## Evaluation Type

**Seminar**

## Scheduled date 1

## Estimated Weekly Independent Workload (in hours)

## Syllabus

Knot theory is a beautiful branch of topology whose basic questions are which types of knots (embeddings of a circle in the 3-space) can be isotoped to the unknot (the standard embedding of the circle as a unit circle in the xy-plane), and how to classify different knots .

Although the questions themselves can be explained to people without mathematical background, the answers and proof techniques tend to be surprisingly sophisticated and are many times related to advanced mathematics and physics.

In this course we shall learn the basic notions of knot theory, and concentrate on knot invariants, which are the main tool for distinguishing between different knots.

We will meet the basic invariants, for example coloring, linking and framing. We will then move to more sophisticated polynomial invariants. We shall then continue to one or more of the following subjects: quantum invariants, Khovanov homology (the categorification of the Jones polynomial), finite type invariants (including Kontsevich's theorem) or the volume conjecture.

## Learning Outcomes

1. The student will know the basic notions of knot theory.

2. The student will study several types of knot invariants and their connections with other areas of mathematics.

## Reading List

1. An introduction to knot theory/Lickorish.

2. Other mathematical survey/research papers for more modern and advanced topics.