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