Seminars & Colloquia Calendar

Download as iCal file

Logic Seminar

Hilbert's Tenth Problem for Subrings of the Rationals

Russell Miller (Queens College)

Location:  Hill 705
Date & time: Monday, 29 January 2018 at 5:00PM - 6:00PM

Abstract:   For a ring \(R\), Hilbert's Tenth Problem \(HTP(R)\) is the set of all polynomials \(fin R[X_1,X_2,ldots]\) for which \(f=0\) has a solution in \(R\). In 1970, Matiyasevich completed work by Davis, Putnam, and Robinson to show that the original Tenth Problem of Hilbert, \(HTP(mathbb{Z})\), is undecidable. On the other hand, the decidability of \(HTP(mathbb{Q})\) remains an open question. We will examine this problem for subrings of the rational numbers, viewing these subrings as the elements of a topological space homeomorphic to Cantor space and connecting their Turing degrees and computability-theoretic properties to those of \(HTP(mathbb{Q})\) itself.

Some of the work discussed is joint with Kramer, and some with Eisentraeger, Park, and Shlapentokh. 

Special Note to All Travelers

Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.

Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.