Course related material and (soon) Videos

Link to all videos uploaded so far

Javier 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
Lecture Notes

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:

Physical Knots (Public Lecture)








Funded by

Organizers:

Simon Blatt - Philipp Reiter - Armin Schikorra