## Abstract

Topological phases of matter entail a prominent research theme, featuring

distinct characteristics that include protected metallic edge states and

the possibility of fractionalized excitations. With the advent of symmetry

protected topological (SPT) phases, many of these phenomena have

effectively become accessible in the form of readily available band

structures. Whereas the role of (anti-)unitary symmetries in such SPT

states has been thoroughly understood, the inclusion of lattice symmetries

provides for an active area of research.

In this talk, I will present a short overview of results on defects in SPT

states that directly motivate the existence of additional physics beyond

the characterization based on (anti-)unitary symmetries. More importantly,

I will then connect these ideas to recent work in which we were able to map

out all different gapped phases of free fermion systems in the presence of

solely lattice symmetries. This revolves around a very simple algorithm

that matches a rather involved mathematical perspective in terms of a

framework called K-theory. I will then discuss the implications of these

combinatorial arguments, such as their impact on the description of Weyl

phases, and sketch related ideas and future perspectives.

## Details

**Talk Number**PIRSA:18010089

**Collection**Condensed Matter

- Condensed Matter

**Scientific Area**

- Scientific Series

**Talk Type**