# Spinors and geometric structures

### APA

Krasnov, K. (2023). Spinors and geometric structures. Perimeter Institute. https://pirsa.org/23040164

### MLA

Krasnov, Kirill. Spinors and geometric structures. Perimeter Institute, May. 01, 2023, https://pirsa.org/23040164

### BibTex

@misc{ pirsa_PIRSA:23040164, doi = {10.48660/23040164}, url = {https://pirsa.org/23040164}, author = {Krasnov, Kirill}, keywords = {Other}, language = {en}, title = { Spinors and geometric structures}, publisher = {Perimeter Institute}, year = {2023}, month = {may}, note = {PIRSA:23040164 see, \url{https://pirsa.org}} }

Kirill Krasnov University of Nottingham

**Talk Type**Scientific Series

**Subject**

## Abstract

I will describe a construction that allows to understand spinors in an arbitrary number of dimensions, with arbitrary signature. I will describe what pure spinors are, and how in low dimensions all spinors are pure. The first impure spinors arise in 8 dimensions, and "purest" impure spinors are octonions. I will describe how a spinor in an arbitrary dimension defines a set of geometric structures. The easiest example of this is how a pure spinor defines a complex structure. As one increases the dimension, the types of geometric structures that are described by spinors become more and more exotic. If time permits, I will describe some examples in 14 and 16 dimensions. Almost nothing is known about spinors in dimension beyond 16.

Zoom link: https://pitp.zoom.us/j/94776499052?pwd=RGVURlRnaEx6REJwVE10VXhqa1Q5Zz09