Title: Asymptotic behavior of lifetime sums of Betti numbers for random simplicial complex processes
Speaker: Shu Kanazawa (Tohoku University)
Abstract: A random simplicial complex process is a family of random simplicial complexes. The Linial--Meshulam complex process and the clique complex process were studied by Hiraoka and Shirai. They showed the exact order of the expected lifetime sum of the Betti numbers for the Linial--Meshulam complex process as the number of vertices goes to infinity. In this talk, I define more general random simplicial complex processes, including the above two models, and report that the exact order of the expected lifetime sum for them was revealed. The key to proving the results is a quantitative generalization of the Cohomology vanishing theorem. This is joint work with Masanori Hino.
Seminar URL: https://math.osu.edu/event-terms-1/seminar-combinatorics
