Our perception of our environment can deceive us. A map, although flat, effectively guides us through a space that, in ...

For example, the surface of a giant doughnut is another 2D space. Through a field called geometric topology, mathematicians like me study all possible spaces in all dimensions. Whether trying to ...

Her research is in geometric and low-dimensional topology. A main theme of her work is using algebraic invariants to detect information about intersections and linking of topological objects. In ...

Such loops are called mathematical knots. Geometric topology is a beautiful and complex subject, and there are still countless exciting questions to answer about spaces. For example, the smooth 4D ...

Whether trying to design secure sensor networks, mine data or use origami to deploy satellites, the underlying language and ideas are likely to be that of topology.