Spinorial and Octonionic Aspects of G2 and Spin(7) Geometry (23w5006)


(University of Waterloo)

Ilka Agricola (Philipps-Universität Marburg, Germany)

(Humboldt University of Berlin)

Sergey Grigorian (University of Texas Rio Grande Valley)

(University of Oxford)


Group Photo

The Banff International Research Station will host the "Spinorial and octonionic aspects of G2 and Spin(7) geometry" workshop in Banff from May 28 to June 2, 2023.

Workshop Files - Slides

Workshop Report - View here

There exists a mysterious algebraic structure in 8-dimensional space that does not behave in the same way as the ordinary arithmetic that we all learn as children. Somewhat surprisingly, this strange algebra, called the octonions, shows up naturally in the study of certain higher dimensional geometric spaces, called manifolds, that are of importance in physics and in the study of the equations introduced by Einstein in general relativity. Geometers have been studying such spaces for a number of years, mostly using tools from calculus and differential equations. The proposed workshops intends to introduce these researchers to experts in the special octonion algebra, as well as in related special algebraic structures called spinors, to facilitate a cross-pollination of ideas, methods, and techniques. Some of these groups have never before been brought together in this way.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).