Thematic Einstein Semester on

Geometric and Topological Structure of Materials

Summer Semester 2021

Speaker


Omer Bobrowski   (Technion)


Title


Homological Connectivity in Random Čech Complexes


Abstract


A well-known phenomenon in random graphs is the phase-transition for connectivity, proved first by Erdős–Rényi in 1959. In this talk we will discuss a high-dimensional analogue of this phenomenon which we refer to as "homological connectivity". Loosely speaking, homological connectivity is the point where the homology of a simplicial filtration stops changing. The model we study is the Čech complex generated over a spatial Poisson point process. We will show that there is a sequence of sharp phase transitions (for different degrees of homology) and also explore the behavior of the complex inside each critical window.



Contact


tes-summer2021@math.tu-berlin.de