Colloquium: A problem with a sense of humor

Speaker: Alexandra Shlapentokh, East Carolina University

In his tenth problem Hilbert asked for an algorithm for determining whether a given polynomial equation in several variables and with integer coefficients has a solution in integers. Matiyasevich, extending work of Davis, Putnam, and Robinson, resolved the problem 70 years later by establishing that it is undecidable. The undecidability of the original problem left the decidability status open for the question about the rationals, Q. This question, now known as Hilbert’s Tenth Problem for Q, remains open today. We will discuss the history and recent developments concerning Hilbert’s Tenth Problem for rings of algebraic integers of number fields.

Short Bio: Alexandra Shlapentokh got her Ph.D. in 1988 at Courant Institute under the direction of Harold N. Shapiro. From 1988-92 she was an Assistant Professor at York College of CUNY, and in 1992 joined East Carolina University in Greenville, NC, where she rose to the rank of Professor. Shlapentokh has authored more than 60 research articles and a Cambridge University Press book. She has given numerous invited talks at logic and number theory meetings, such as Logic Colloquium, ASL meetings, Hausdorff Institute Diophantine Equations Trimester workshop and ETH Abelian Varieties Semester workshop.  She has also been a co-organizer of many meetings and workshops, including those in Oberwolfach and at AIM.  Currently, she is a co-organizer of Definability, Decidability and Computability in Number Theory semester at MSRI in Berkeley in Fall 2020.