Omer Bobrowski - Random Simplicial Complexes, Lecture I

Explore the fascinating world of random simplicial complexes in this comprehensive lecture, the first in a series. Delve into the higher-dimensional generalization of graphs, examining their growing importance in modern data and network analysis. Learn about the two most well-studied models: the random d-complex and the random Cech complex. Discover how these structures extend random graph theory, investigating phenomena such as connectivity, cycle formation, and the emergence of "giant" connected components. Gain insights into algebraic topology and homology theory as essential tools for understanding these complex structures. Begin with an introduction to random simplicial complexes and simplicial homology, setting the foundation for deeper exploration in subsequent lectures. No prior knowledge is required for this accessible yet in-depth examination of this cutting-edge mathematical field.

Introduction
Background
Models
Simplicial Complex
Notation
homology
cohomology
Two models
Poisson process