Program
Introduction to Modern Knot Theory
Student No.:50
Time:Wed./Fri. 13:30-15:00pm; Seminar 2012-09-10/17/24/27 Mon. 13:30-15:00pm
Instructor:Manturov Vassily Olegovich  [People's Friendship University of Russia]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2012-9-5
Ending Date:2012-9-28

Description:

Knot theory studies immersions of a circle (collection of circles) into three-space up to isotopy. In the last few decades, new ideas coming from various branches of mathematics and physics have completely change the shape of knot theory. We are going to touch to both combinatorial and geometric aspect of knot theory.

 

This will be a four week introductory course on core materials in knot theory. Every week we have two ninety minutes lectures with a following up seminar. In the seminar we discuss research projects including unsolved problems around the material being lectured. Little prerequisite is needed to access the material of the course. The course invites both graduate students and undergraduate students who are enthusiastic in math or curious about knot theory to attend.

 

The video is available now, you can access by visiting ftp://166.111.25.49/ in the browser or using a ftp software(for the video file is more than 1G, using a ftp software is highly recommended). The username and password are both "msclecture". You can download the ftp software from http://filezilla-project.org/ or an old portable version from MSC.

 

Content of the course (tentative)

1st week

1. Reidemeister moves, linking number, coloring invariant and unknotting number.

2. Kauffman bracket, minimality theorems for knots and links and virtual knots.

 

2nd week:

1. Link invariants coming from braids.

2. Vassilliev invariants.

 

3rd week:

1. Categorification for knots--Khovanov homology.

2. Categorification for knots--Heegaard Floer homology.

 

4th week:

1. Parity and simplest applications.

2. Parity, cobordism and projections.

 

Prerequisite:

 

 

Reference:

V.O.Manturov, Knot theory, CRC-Press, Boca Raton, 416 pp. 2004.

D.P.Ilyutko, V.O.Manturov, Virtual Knots. The State of The Art. World Scientific.