ICTP Math Associates Seminar (Zoom Meeting) - Thursday 10 October at 16:00 (José Cisneros-Molina)

[ICTP Math Section]

Math Associates Seminar


Thursday 10 October 2020, at 16:00, Central European Time



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Speaker: José Cisneros-Molina (UNAM, Mexico)


Title: Exotic Spheres and Singularities


Abstract:
Milnor's fibration theorem is a landmark in singularity theory, it 
allows to deepen the study of the geometry and topology of analytic maps 
near their critical points. To each singular point of a complex 
hypersurface it associates a fibre bundle, known as the Milnor Fibration 
of the singularity.
The birth of Milnor's Fibration Theorem is a curious story, since its 
origin is not in Singularity Theory. It begins with the discovery by 
Milnor in 1956 of the first exotic spheres": smooth 7-manifolds 
homeomorphic to the standard 7-sphere, but with non-equivalent 
differentiable structures. Later, work of some great  mathematicians 
like Brieskorn, Jänich, Hirzebruch and Pham, led to the discovery of 
some examples of complex hypersurface singularities whose links are 
exotic spheres. This motivated Milnor to determine when the link of a 
complex hypersurface singularity is a homotopy sphere, culminating in 
his now famous book "Singular points of complex hypersurfaces". One of 
the main results in this book is precisely Milnor's Fibration Theorem.
The aim of this non-technical talk is to tell this interesting story.