Homology of simplicial geometric complexes associated with random graphs.

• Grant number: 24/21482-8
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: July 01, 2025
• End date: January 31, 2028
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Cristian Favio Coletti
• Grantee: Luciano Henrique Lacerda de Araújo
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil
• Associated research grant: 23/13453-5 - Stochastic systems modeling, AP.TEM

Abstract

The purpose of this doctoral project is to study topological invariants of random graphs. As the main result, we propose that the candidate demonstrate the Strong Law of Large Numbers and the Central Limit Theorem for the dimension of the homology groups of random graphs obtained from the Bernoulli independent edge percolation model. (AU)