The self-assembly of objects with a set of desired properties is a major goal of material science and physics. A particularly challenging problem is that of self-assembling structures with a target ...

Three high schoolers and their mentor revisited a century-old theorem to prove that all knots can be found in a fractal called the Menger sponge. In the fall of 2021, Malors Espinosa set out to devise ...

Hyperbolic knot theory concerns itself with the study of knots and links embedded in three‐dimensional spaces that admit hyperbolic structures. The geometry of a link complement—the manifold that ...

Deciding whether a knot is fit to be tied just got a bit more scientific. Some knots are stronger than others, but scientists have struggled to explain why. Now, with the help of color-changing fibers ...

Sometimes, a simple, even childish question turns out to be connected to the deepest secrets of the universe. Here’s one: How many different ways can you tie your shoelaces? Mathematicians have been ...

Low-dimensional topology, hyperbolic geometry and 3-manifolds, knot theory, contact geometry, curve complex and mapping class group. Low-dimensional topology, hyperbolic geometry and 3-manifolds, knot ...