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Generalizations of Hilbert's Tenth Problem

Model Theory in Geometry and Arithmetic May 12, 2014 - May 16, 2014

May 15, 2014 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Kirsten Eisentraeger (Pennsylvania State University)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

v1150

Abstract

In 1970 Matiyasevich, building on work by Davis, Putnam and Robinson, proved that Hilbert's Tenth Problem is undecidable. Since then, analogues of this problem have been studied by considering polynomial equations over commutative rings other than the integers. The biggest open problem in the area is Hilbert's Tenth Problem over the rational numbers. In this talk we will construct some subrings $R$ of the rationals that have the property that Hilbert's Tenth Problem for $R$ is Turing equivalent to Hilbert's Tenth Problem over the rationals.

We will also discuss some recent undecidability results for function fields of positive characteristic.