2018-2019 Ithaca High School maths seminar 2: Introduction to Knot Theory

Instructor: Hannah Keese
hrk49 at cornell dot edu

Notes for the class:

Computing the Alexander polynomial using Seifert surfaces


A list of possible projects can be found here

Computing the Jones polynomial

Jack Greenberg, Alex Mueller and Jeffrey Lantz wrote a program that computes the Jones polynomial for knots and links given a braid word, and visualises complete resolutions of knots.
You can find their program here.

Seifert surfaces

Zoë Marschner, Dora Kassabova and Kasia Fadeeva learnt about Seifert surfaces and knot invariants that are computed from them. As part of this project, they wrote a program that draws a Seifert surface given a user-drawn knot. It also computes the genus of the surface and the Alexander polynomial of the given knot.
You can find their program here.
Here is their output for the knot 5_1: