Asymptotic combinatory: Extremal problems and extracombinatorial methods

• Grant number: 25/10103-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2025
• End date: July 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Sinai Robins
• Grantee: Caio Simon de Oliveira
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 23/03167-5 - Classical, asymptotic, quantum and geometric combinatorics, AP.TEM

Abstract

This project aims to study Functional Graphs of alpha-maps in Dedekind Domains, with emphasis on integers. In particular, we study and characterize the isomorphism classes of such graphs, together with their algebraic and number theoretic implications.Thus, Caio will acquire specific knowledge in the area of asymptotic combinatorics, with emphasis on extremal problems and extracombinatorial methods, involving algebraic, analytical, geometric, topological and linear and nonlinear optimization techniques. (AU)