# PDEs and applications seminar: Anyons on networks from a geometric perspective

- Date: –11:15
- Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
- Lecturer: Tomasz Maciążek
- Organiser: Matematiska institutionen
- Contact person: Kaj Nyström
- Seminarium

Abstract: In quantum systems confined to two spatial dimensions (quasi)particles that are neither bosons nor fermions may exist. Such particles are called anyons. They proved to be key elements of physical models realising so-called topological states of matter. Notably, the existence of anyons is also possible in (locally) one-dimensional systems that are networks. In my talk, I will show how braiding properties of anyons on networks relate to the well-known braiding properties of anyons on the plane. I will also point out some significant simplifications that come from considering anyons on networks in relation to the classification of many-particle quantum statistics. Throughout my talk, I will show many intuitive examples illustrating how anyons can braid on small networks. My analysis is fully topological and independent of the particular physical model of anyons. I will argue that networks can be sources of very robust and versatile geometries that provide more freedom for the particle exchange than traditional two-dimensional settings.

Note: the speaker will also give a talk in the KTH/SU topology seminar on Thursday March 12 at 10:15 on the topic "Homology groups of graph configuration spaces".