Mark Bodner (MIND Research Institute, USA)

Affine reflection groups for tiling applications: knot theory and DNA

Abstract:
   In this talk some non-conventional applications of affine Weyl groups WAff of rank 2 (the symmetry group of the tiling/lattice) will be presented. First tools for applications requiring tilings of the real Euclidean plane will be briefly developed and presented. Then a correspondence between such tilings and 2-dimensional projections of knots will be elucidated. The resulting mathematical structure provides a framework within which is encompassed recent work utilizing knot theory for modeling the structure and function of genetic molecules. Particularly, the determination of the action of specific enzymes in altering the topology and geometry of DNA in site-specific recombination will be addressed within this mathematical framework.