**Title of the course:** A quick course in knot theory

**Instructor:** Dr. Neslihan Güğümcü

**Institution:** National Technical University of Athens

**Dates:** 9-15 July 2018

**Prerequisites:** -

**Level:** Graduate, advanced undergraduate, beginning undergraduate

**Abstract:** Knots have been objects of mathematics since the 18th century. Today the theory of knots is a developed theory lying in the branch of algebraic topology and it interrelates with many other areas such as mathematical physics, physics, biology and chemistry. In this course, we will learn the basics of the theory of knots. The outline of the course will be mostly as follows.

Day 1: Basic concepts of algebraic & geometric topology

Day 2: Knots and links in mathematics: an overview discussion and formal definitions and basic theorems

Day 3: Simple invariants of knots and links

Day 4: Some polynomial invariants of knots and links

Day 5: The Jones polynomial and the Kauffman bracket

Day 6: Other knotted objects; An introduction to the theory of braids and tangles, Applications of the knot theory to biology, physics and chemistry

**Language: **TR, EN