Geometric intersection graphs form an intriguing class of structures in which vertices represent geometric objects – such as line segments, discs, or curves – and an edge is established between two ...

Vertices arrive sequentially in space and are joined to existing vertices at random according to a preferential rule combining degree and spatial proximity. We investigate phase transitions in the ...

What if artificial intelligence (AI) could be used to spur discovery in areas such as biotechnology, drug discovery and fluid dynamics? Using geometric graphs and innovative methodologies, AI can ...

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 ...

Ancient Babylonians charted Jupiter’s heavenly motion in a surprisingly modern, mathematically abstract way — a feat that until now was thought to have originated among European scholars who lived ...

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of recent work by the ...