Professor in Algebraic Geometry
Mathematics is a general science concerned with problem solving and the development of methods and has given rise to countless discoveries throughout history. Developments in the area are advancing at a rapid pace, not least when it comes to increasing understanding of different geometric objects.
David Rydh’s research area is algebraic geometry that has its roots in advances made by scientist René Descartes as far back as the 17th Century. By introducing a coordinate system, he was able to link algebraic equations with geometric objects. This opened the door to expanding the field of geometry to describe other shapes in the form of curves.
Within algebraic geometry, moduli theory is used to classify curves and here, the concept of stacks has gained a central function. The smallest element in a stack is a point, but the point itself has internal symmetries: a symmetry group. By way of analogy, stacks can be likened to crystals where every point in the stack corresponds to an atom and the symmetry group to the atomic number. Just as all atoms have been classified into the periodic table, all groups (both finite and infinite) have been classified.
Together with other researchers, Rydh has advanced knowledge about stacks and symmetry groups, such as via the development of new algorithms. As a result, this has made it possible to effectively describe and treat stacks with the aid of more classic geometric objects and methods, that have a large number of applications, primarily within moduli theory.