Workshop on Topology: Identifying order in complex systems

The space of all positions of n disks of radius r in a bounded region has long been studied from the points of view of statistical mechanics and probability. A phase transition is known to occur from simulations, but this is still mysterious to...

The ordinary homology of a subset S of Euclidean space depends only on its topology. By systematically organizing homology of neighborhoods of S, we get quantities that measure the shape of S, rather than just its topology. These quantities can be...

This will be a report on topics related to topological complexity (TC), introduced by Michael Farber in 2003 as a numerical measure of the complexity of robot motion planning problems. TC of real projective space P^n (lines through the origin in...

Optical fields propagating in three-dimensional free space are complex scalar fields, and typically contain nodal lines (optical vortices) which may be thought of as interference fringes. Random wave fields, representing speckle patterns randomly...