Milen Yakimov

Sponsor: National Science Foundation

Quantum Cluster Algebras and Monoidal Categories  

Most mathematical models in science and engineering assume variables that commute — that order doesn’t matter — but quantum mechanics broke that assumption and raised hard problems about structures where it fails. This project investigates two families of these noncommutative objects, quantum cluster algebras at roots of unity and monoidal categories, building the tools needed to understand their internal structure and how they act on other mathematical spaces.