Omer Bobrowski - Random Simplicial Complexes
Explore the fascinating world of random simplicial complexes in this third lecture of a minicourse series. Delve into the random Cech complex, a higher-dimensional generalization of the random geometric graph. Learn about connectivity, formation of cycles, and emergence of "giant" connected components in this context. Compare these higher-dimensional phenomena to their lower-dimensional graph counterparts using algebraic topology and homology theory. Gain insights into the Chair Complex, D Complex, Curly Age, and Mode Theory. Examine the differences between connectivity and homological connectivity, and understand the concepts of giant components and giant cycles. Discover the duality theorem and its implications. No prior knowledge is required for this comprehensive exploration of random simplicial complexes and their applications in modern data and network analysis.