ICTP Math Associates Seminar (Zoom Meeting) - Thursday 10 October at 16:00 (José Cisneros-Molina)
ICTP Math Section
math at ictp.it
Thu Oct 1 10:25:54 CEST 2020
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
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.
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