# On the classification of topological phases

### APA

Johnson-Freyd, T. (2020). On the classification of topological phases. Perimeter Institute. https://pirsa.org/20060018

### MLA

Johnson-Freyd, Theo. On the classification of topological phases. Perimeter Institute, Jun. 01, 2020, https://pirsa.org/20060018

### BibTex

@misc{ pirsa_PIRSA:20060018, doi = {10.48660/20060018}, url = {https://pirsa.org/20060018}, author = {Johnson-Freyd, Theo}, keywords = {Mathematical physics}, language = {en}, title = {On the classification of topological phases}, publisher = {Perimeter Institute}, year = {2020}, month = {jun}, note = {PIRSA:20060018 see, \url{https://pirsa.org}} }

Theo Johnson-Freyd Dalhousie University

**Collection**

**Talk Type**Scientific Series

**Subject**

## Abstract

There is a rich interplay between higher algebra (category theory, algebraic topology) and condensed matter. I will describe recent mathematical results in the classification of gapped topological phases of matter. These results allow powerful techniques from stable homotopy theory and higher categories to be employed in the classification. In one direction, these techniques allow for complete *a priori* classifications in spacetime dimensions ≤6. In the other direction, they suggest fascinating and surprising statements in mathematics.