New algebraic minimal models for topological spaces

This project aims to develop new concepts of minimal models for objects with multiplicative structures that arise in the mathematical fields of algebra and topology.

Geometric objects can often be studied effectively by assigning algebraic invariants to them, which capture the essence of their structure. In many interesting cases, these algebraic invariants can be represented as differential graded algebras. However, the differential graded algebras that arise from geometry are often quite large and complex. Using minimal models has proven to be a successful strategy for simplifying these large differential graded algebras into more manageable structures. The goal of this project is to use diagrams indexed by finite sets and injections to construct minimal models in contexts that are currently beyond the reach of existing methods.