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.

# Counting knotted curves and surfaces in lattices

Speaker:

Stu Whittington (Toronto)

Date/Time:

Mon, 28/02/2011 - 16:30

Room:

M103

Seminar series: