Geometry from quantum matter and quantum matter from geometry

Abstract: Geometry is inseparable from the visual world. We have come to understand, however, that nature leverages geometry at other length scales. In particular, the last decade has seen the dawn of a new age of “quantum matter” in which topology and geometry play a key role at microscopic scales. A good understanding of how geometry manifests here leads to the potential for new materials and physical systems that leverage more exotic geometries. This is not only an opportunity for pure mathematicians to interact with physics in new ways, but also to reconsider how we engineer and print materials at nanoscales. As these research directions take shape, there are increasingly many opportunities for research contributions by students. I will describe the ideas at play and how researchers and students in the quanTA Lab in the west of Canada are putting these ideas in motion.

Mathematics

Audience: learners

Geometry Labs United Seminar

Series comments: Monthly seminar for the Geometry Labs United network, including members and interested parties. We start with a 20-minute general-audience talk on Zoom, and then have 40 minutes to talk in breakout rooms. Past talks can be found at geometrylabs.net/category/seminar/.