Peter Jørgensen’s research is in algebra, which is one of the main branches of pure mathematics. At heart, algebra is the study of equations. It has wide perspectives because equations have links to other parts of mathematics. For example, the equation x2+y2=1 describes a circle, which is part of geometry. Another example is the algebraic expression n(n-1)/2 which is relevant to combinatorics; it tells us in how many ways we can choose two different items from a collection of n items.
The research project of Peter Jørgensen’s DNRF Chair concerns Calabi-Yau categories. These categories are complicated algebraic objects which arise in several different branches of mathematics, not least geometry and combinatorics. They even play a key role in physics where they are crucial objects of modern quantum field theory.
The study of Calabi-Yau categories has been an important direction of Peter Jørgensen’s research for some time. One of his most highly cited papers showed how these categories arise from topological spaces with Poincaré duality; such spaces are ubiquitous in geometry. He has also proved a number of combinatorial results on Calabi-Yau categories.
Peter Jørgensen is currently studying invariants and symmetries of Calabi-Yau categories. A long-term goal is to develop these tools to a level where it becomes feasible to produce lists of all possible Calabi-Yau categories; this is referred to as classification. In turn, being able to refer back to such lists will provide crucial information for all branches of mathematics where Calabi-Yau categories arise.