Connectivity and percolation are two well studied phenomena in random graphs.
In this talk we will discuss higher-dimensional analogues of connectivity and percolation that occur in random simplicial complexes.
Simplicial complexes are a natural generalization of graphs that consist of vertices, edges, triangles, tetrahedra, and higher dimensional simplexes.
We will mainly focus on random geometric complexes. These complexes are generated by taking the vertices to be a random point process, and adding simplexes according to their geometric configuration.
Our generalized notions of connectivity and percolation use the language of homology - an algebraic-topological structure representing cycles of different dimensions.
In this talk we will discuss recent results analyzing phase transitions related to these topological phenomena.
Further Information
Omer Bobrowski, an electrical engineer and mathematician, is an Associate Professor in the Viterbi Faculty of Electrical and Computer Engineering at the Technion -