Homological conjectures via Algebras Extentions

• Grant number: 25/19298-7
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: October 01, 2025
• End date: October 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Eduardo do Nascimento Marcos
• Grantee: Roger Ramirez Primolan
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 24/14914-9 - Structures and representations of algebraic systems and their applications, AP.TEM

Abstract

In this research project, we will tackle homological problems within finite-dimensional algebras and quiver representation theory. We are interested in conjectures such as Han's conjecture and the central finitistic dimension conjecture. We intend to approach this problem through extensions of algebras, more precisely, via the relative homological theory developed by Hochschild. This century, particularly in the last decade, several articles have explored this area of research with considerable success. We intend to break this difficult problem into two interrelated parts: the study of techniques that allow us to work with the theory developed by Hochschild. Specifically, we will attempt to construct relative versions of the Igusa-Todorov functions and the delooping level invariant, and the application of these techniques and the intuition gained to advance homological conjectures for finite-dimensional algebras. (AU)