Genericity of o-minimality for smooth functions
| Dates: | 15 May 2019 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Adults, Alumni, Current University students |
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| Speaker: | Olivier Le Gal |
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Join us for this research seminar, part of the Logic seminar series.
We give an explicit condition on the Taylor developments of a smooth real valued function \(f\) defined on a compact interval I, which insures that the expansion\(\mathcal R =<\mathbb{R},0,1,+,\times,\le ,f>\) of the field of reals with \(f\) is o-minimal and polynomially bounded. This condition happens to be generic with respect to the Whitney topology on \(C^{\infty}(I,\mathbb R)\). It implies that any generic property of smooth functions can be realized in an o-minimal structure; for instance, there are o-minimal structures that defines nowhere analytic smooth function (already proven by Rolin, Speissegger and Wilkie), or o-minimal structure that are incompatible with the structure of global subanalytic sets.
Speaker
Olivier Le Gal
Organisation: Université de Savoie
Travel and Contact Information
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Frank Adams 1
Alan Turing Building
Manchester
