Student seminar in pure mathematics
Summary
In this seminar we will study the foundations of Knot theory, which studies entanglements of closed curves in three dimensional space. What seems like a simple subject in topology turns out to be a rich theory with applications to 3-manifolds, representation theory, physics and much more.
Content
- Basics of Knot theory: Link Diagrams, Reidemeister moves, Seifert surfaces
- Knot Invariants: Jones-, Alexander and HOMFLY-Polynomial
- 3-Manifold Invariants
- Connections with Representation theory
Learning Prerequisites
Recommended courses
- Introduction to differentiable manifolds
- Algebraic topology
- Rings and Modules
Learning Outcomes
By the end of the course, the student must be able to:
- Demonstrate their knowledge about knots and links.
Transversal skills
- Make an oral presentation.
- Write a scientific or technical report.
- Access and evaluate appropriate sources of information.
Teaching methods
Each participant will give a lecture on a subject in knot theory. The lecture is complemented by the professor and exercise sessions.
Expected student activities
Prepare a lecture, write lecture notes and solutions to exercises. Active participation during class and exercise sessions.
Assessment methods
The grade will depend on the participants oral presentation and written reports. There will be no final exam.
Resources
Bibliography
An Introduduction to Knot Theory by R. Lickorish.
Ressources en bibliothèque
In the programs
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Student seminar in pure mathematics
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Student seminar in pure mathematics
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Student seminar in pure mathematics
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Student seminar in pure mathematics
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
Reference week
Mo | Tu | We | Th | Fr | |
8-9 | |||||
9-10 | |||||
10-11 | |||||
11-12 | |||||
12-13 | |||||
13-14 | |||||
14-15 | |||||
15-16 | |||||
16-17 | |||||
17-18 | |||||
18-19 | |||||
19-20 | |||||
20-21 | |||||
21-22 |
Légendes:
Lecture
Exercise, TP
Project, other