Differential Geometry Working Seminar

Jean-Pierre Bourguignon, President, European Research Council

"What is a spinor?"

Note: This is a *pre-recorded lecture* which was given as part of the Maxwell Institute's "Atiyah Lecture Series" in Edinburgh on January 11, 2021. We plan to watch the recorded lecture together (in-person and/or on Zoom, as usual this term) and we can pause the video at any moment to ask each other questions and hopefully get meaningful answers from each other. The video is available here: https://www.icms.org.uk/events/event/?id=1128

Abstract: This was the title of the lecture Sir Michael gave in September 2013 at IHES on the occasion of the farewell conference for my retirement as Director. This was most appropriate as I learned a lot from him about this subject. It is true that mathematicians struggled for a long time to get acquainted with spinors. It is in sharp contrast with the fact that physicists adopted them without hesitation as soon as Paul-Adrien Maurice Dirac showed they were essential to formulate a quantum equation invariant under the Poincaré group. Indeed spinors have a number of features that make them both subtle and powerful to deal with mathematical problems. Of great importance are of course the natural differential operators universally defined on spinor fields, namely the Dirac and the Penrose operators. The purpose of the lecture is to revisit historical steps taken to master these objects, explore their remarkable geometric content and present some mathematical problems on which they shed light.

This seminar will be held jointly online and in person:

• Zoom link: https://uwaterloo.zoom.us/j/95873618652?pwd=OENSeFdERzUzV2NkM3hjQ0F1MzFYUT09
• Room: MC 5403