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A Limit Theorem for Betti Numbers of Random Simplicial Complexes

Offered By: Applied Algebraic Topology Network via YouTube

Tags

Algebraic Topology Courses Law of Large Numbers Courses Betti Numbers Courses

Course Description

Overview

Explore a 24-minute lecture on the asymptotic behavior of Betti numbers in homogeneous and spatially independent random simplicial complexes. Delve into the extension of the Erdős–Rényi graph model to higher-dimensional structures, examining the law of large numbers for Betti numbers of Linial–Meshulam complexes. Discover the key role of local weak convergence in simplicial complexes and its application in establishing the local weak limit theorem for these random structures. Follow the presentation's outline, covering the random complex model, main results, proof techniques, and concluding with a Q&A session.

Syllabus

Introduction
Outline
Random Complex Model
Results
Proof
Main result
Questions


Taught by

Applied Algebraic Topology Network

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