Differential Geometry Working SeminarExport this event to calendar

Wednesday, June 15, 2022 — 9:30 AM EDT

Talk #1 (9:30am - 10:30am): Anton Iliashenko, Department of Pure Mathematics, University of Waterloo

"Some results about Riemannian submersions"

We will go through some results about Riemannian submersions from the Arthur L. Besse's book on Einstein manifolds. For example, we will show that a surjective Riemannian submersion is harmonic iff the fibers are minimal, and some others as the time permits.


Talk #2 (10:45am - 12:15pm): Jean-Pierre Bourguignon, President, European Research Council

"What is a spinor?"

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.

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 watched the first half of the lecture two weeks ago, and we will watch the rest of it this time. As we did last time, we will pause the video at any moment to ask each other questions and hopefully get meaningful answers from each other. We watched the first half in Fall 2021, but never finished it, and there's been a lot of turnover in our audience, so we'll just watch the whole talk from the beginning.

The video is available here: https://www.icms.org.uk/events/2021/inaugural-atiyah-lecture-jean-pierre-bourguignon

MC 5403

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