This lecture course is devoted to the study of random geometrical objects and structures. Among the most prominent models are random polytopes, random tessellations, particle processes and random ...

Keep Learning is available to stream on pbs.org and the free PBS App, available on iPhone, Apple TV, Android TV, Android smartphones, Amazon Fire TV, Amazon Fire Tablet, Roku, Samsung Smart TV, and ...

Geometric objects take on different properties depending on the space in which you visualize them. Using techniques from an upstart field called tropical geometry — which analyzes complicated shapes ...

The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called flip. This space is a ...

David Conlon and Asaf Ferber have raised the lower bound for multicolor “Ramsey numbers,” which quantify how big graphs can get before patterns inevitably emerge. “There is no absolute randomness in ...