From Ideals to Quantum Spaces

In mathematics, a fundamental pursuit is the classification of mathematical objects, such as set, shapes, and functions, in a way that captures their essential characteristics without redundancy. This endeavor relies on the notion of invariants, which, akin to barcodes, encapsulate essential characteristics of these entities. For quantum spaces, this classification presents several challenges and has progressed only on a case-by-case basis. We strive to understand the structure and invariants of these spaces across a broader spectrum. To achieve this, we follow the mathematical principle of duality and employ the tools of noncommutative geometry—a discipline profoundly influenced by quantum theory. Read more.