Logic seminar: Sylvy Anscombe
| Dates: | 1 May 2024 |
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| Times: | 15:15 - 16:30 |
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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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Title: Uniformities for Hilbert's Tenth Problem in henselian valued fields
Abstract
Hilbert's Tenth Problem in its original form asks for an algorithm to
determine correctly whether -- or not -- a given multivariable
polynomial equation with integer coefficients has integer solutions.
The surprising resolution, by Davis, Putnam, Robinson, and finished by
Matiyasevich in 1970, is that there is no such algorithm. In the
terminology of mathematical logic, the existential theory of the ring
of integers is undecidable. I am interested in the (un?)decidability
of the existential theories of a variety of rings and fields,
especially of "large" fields, for example those fields admitting a
non-trivial valuation that satisfies "Hensel's Lemma", a weak form of
completion. In this talk I'll describe work in this direction (joint
with Dittmann, Fehm, Jahnke, and others, in various combinations), new
"uniform" results, and some links with theories of function fields.
Travel and Contact Information
Find event
Frank Adams 1 (and zoom, link in email)
Alan Turing Building
Manchester
