### The belt trick and spin groups

- Series
- Geometry Topology Student Seminar
- Time
- Wednesday, March 29, 2023 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Sean Eli – Georgia Tech – dminahan6@gatech.edu

This talk includes an interactive prop demonstration. There exist non-trivial loops in SO(3) (the familiar group of real life rotations) which can be visualized with Dirac's belt trick. Although the belt trick offers a vivid picture of a loop in SO(3), a belt is not a proof, so we will prove SO(n) is not simply connected (n>2), and find its universal covering group Spin(n) (n >2). Along the way we'll introduce the Clifford algebra and study its basic properties.