Functions with no critical points

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• Oscar Randal-Williams (Cambridge)
• Thursday 10 October 2024, 16:00-17:00
• CMS MR2.

If you have a question about this talk, please contact HoD Secretary, DPMMS.

The critical points of a generic smooth function on a manifold, perhaps satisfying boundary conditions, are closely related to the topology of the manifold. Some manifolds however (e.g. M x [0,1]) admit smooth functions with no critical points (e.g. projection to the second factor). In this case it is a central problem in the study of diffeomorphism groups to understanding the topology of the space of all such functions. I will explain some older and more recent approaches to this problem, and the surprising connections it has with other mathematical objects.

The talk will be followed by a wine reception in the central core.

This talk is part of the DPMMS Departmental Colloquia series.

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