School of Mathematical Sciences

Counting knotted curves and surfaces in lattices menu

Counting knotted curves and surfaces in lattices

Stu Whittington (Toronto)
Mon, 28/02/2011 - 16:30
Seminar series: 

Simple closed curves can be knotted in 3-space and these knots
can be seen experimentally in circular DNA molecules, where the
entanglements affect cellular processes.  It has 
been known for over twenty years that the knot probability 
goes to unity as the size increases.  It is natural to ask what
happens in higher dimensions.  2-spheres can be knotted in 4-space
and one might ask if the knot probability goes to unity as the 
area of the 2-sphere increases.  This seminar will first 
review the situation in three dimensions, then discuss why the 
higher dimensional case is more difficult and why the lower
dimensional argument fails in 4-space.  Finally we shall discuss
some results in this direction where the 2-sphere is confined
to a tube in the 4-dimensional hypercubic lattice.