Course related material and (soon) Videos
Link to all videos uploaded so farJavier Arsuaga/Mariel Vazquez
- 1. Introduction to DNA topology: enzymes that unknot and unlink DNA by local reconnection and local crossing changes (Tutorial Slides)
- 2. The tangle method: Modeling local reconnection using band surgery
- 3. Analysis of DNA packing in viruses using random knotting
- 4. Random linking of minicircles in trypanosomes
Keith Moffatt
- 1. Helicity and its role in dynamo theory
- 2. Relaxation under topological constraints
- 3. Minimum energy states of knots and links
- 4. Topological jumps of minimum area soap-films
Radmila Sazdanović
- 1. Introduction to Khovanov link homology (Slides)
- 2. More on Khovanov homology (Slides)
- 3. Torsion in Khovanov link homology (Slides)
- 4. Quantum invariants of links and 3-manifolds
Paweł Strzelecki/Heiko von der Mosel:
- 1. Introduction: regularity of finite energy curves.
- 2. Average crossing number estimates and other corollaries of regularity.
- 3. Characterizing finite energy curves
- 4. Symmetric critical knots
Louis H. Kauffman
Physical Knots (Lecture Series)
This talk is a tour of visual ideas relating knots to situations in natural science. We will begin with knots and DNA and the production of knots in DNA recombination. Then we will show a movie of knotted vortices in water (courtesy of the work of William Irvine at the University of Chicago). Irvine and his group accomplished a feat that is the equivalent of blowing a knotted smoke ring! We discuss the possibility of knotted gluon fields in relation to the complexity of knots measured by rope length. We discuss the possibility of framed braids as a basis for elementary particles. And, time permitting, we discuss the pioneering work of Edward Witten on the nature of knot invariants.
Links and References:
- New Invariants in the theory of knots
- Statistical mechanics and the knot polynomial An Introduction to Khovanov Homology
- Three-Dimensional Topology and Quantum Physics
- Physical Knots