Volodymyr Mazorchuk will receive funding for a postdoctoral position for international researchers at his group at the Department of Mathematics, Uppsala University.
A common way to solve a mathematical problem is to first study its simplification. However, it often leads to a situation in which some useful information is lost. In order to develop a more sophisticated theory you often need to go back and transform the simplified problem into a more complex one.
This process is at work in the category theory, a branch of modern mathematics developed after the Second World War. The theory translates large areas of mathematics into a more general setting. Such upgrading of concepts from one area of mathematics to more general concepts is called categorification.
Reformulating mathematics into a more abstract setting can reveal a common structure in several seemingly unrelated fields of study. For example, categorification of the so-called Khovanov homology led to the development of a new theory, called higher representation theory.
Khovanov homology was developed in order to study ways to distinguish different knots. A knot can be imagined as a string with its ends melded together. Knot theory, an active area of research, finds its applications, among others, in the theory of low-dimensional spaces. One of the goals of the Uppsala group’s research is to generalize the higher representation theory, and thus lay foundations to its abstract version.