In this paper we study the treewidth of the random geometric graph, obtained by dropping n points onto the square [0, √n]² and connecting pairs of points by an edge if their distance is at most r = ...

Geometric Function Theory is a vibrant field that investigates the geometric properties of analytic functions, including univalence, starlikeness, and convexity, which are key to understanding their ...

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 ...

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 ...

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 ...