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SUMMARY:Sylvy Anscombe (Paris)
DTSTART:20240430T130000Z
DTEND:20240430T140000Z
DTSTAMP:20260421T154246Z
UID:UEAPS/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UEAPS/27/">U
 niformities for Hilbert's Tenth Problem in henselian valued fields</a>\nby
  Sylvy Anscombe (Paris) as part of ANTLR seminar\n\nLecture held in NEWSCI
  0.04.\n\nAbstract\nHilbert's Tenth Problem in its original form asks for 
 an algorithm to determine correctly whether -- or not -- a given multivari
 able polynomial equation with integer coefficients has integer solutions.\
 nThe surprising resolution\, by Davis\, Putnam\, Robinson\, and finished b
 y Matiyasevich in 1970\, is that there is no such algorithm. In the termin
 ology of mathematical logic\, the existential theory of the ring of intege
 rs is undecidable. I am interested in the (un?)decidability of the existen
 tial theories of a variety of rings and fields\, especially of "large" fie
 lds\, for example those fields admitting a non-trivial valuation that sati
 sfies "Hensel's Lemma"\, a weak form of completion. In this talk I'll desc
 ribe work in this direction (joint with Dittmann\, Fehm\, Jahnke\, and oth
 ers\, in various combinations)\, new "uniform" results\, and some links wi
 th theories of function fields.\n
LOCATION:https://researchseminars.org/talk/UEAPS/27/
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