# An Analyst's Path to Quantum Symmetry

## About the project

The word* symmetry* is of ancient Greek origin. The Greeks interpreted

this word as the harmony of different parts of an object, the good proportions between its constituent parts. A more formal contemporary meaning of symmetry is invariance of an object under some kind of transformations. In mathematics the idea of symmetry has taken more abstract forms, leading among other things to the notion of a *quantum group*. Quantum groups generalize the idea that a collection of transformations define a symmetry, but now such a collection exists as a whole and no transformation makes sense individually. While this may sound abstract, one of the motivations behind quantum groups is to understand symmetries in nature at the subatomic level, where the laws of physics behave in a very bizarre way from our macroscopic point of view. When one studies quantum groups, it turns out that it is useful to think about even more abstract structures, so called *tensor categories*, which describe symmetries not of separate objects,

but, in some sense, of their core common idea. The goal of the project is to develop analytical tools to study these abstract structures and as application get a much better understanding of quantum groups.

## Financing

This project is financed by the Reseach Council of Norway. Funding ID: 300837, total budget 15,7 million NOK.