Conference: 51st Arkansas Spring Lecture Series in the Mathematical Sciences

University Of Arkansas, Fayetteville AR

Investigators

Abstract

This award supports participation in the 51st Arkansas Spring Lecture Series, which will take place from January 28-30, 2026 at the University of Arkansas in Fayetteville, Arkansas. The conference brings together world experts and young career mathematicians, and is centered on a lecture series given by Bjorn Poonen of the Massachusetts Institute of Technology on "Undecidability related to arithmetic geometry.” This topic is central to pure mathematics and has practical applications toward the question of when there are algorithms that determine integer roots of systems of polynomial equations. The problem of the existence of such algorithms is centuries old, going back to Hilbert, yet recent work has exploded in the area, bringing together a tour de force from many areas of mathematics. The conference features a unique mix of lectures, problem discussions, workshops, and a public lecture aimed at expanding mathematical appreciation to the public at large. Hilbert's tenth problem was resolved in the negative, concluding that there is no algorithm to determine when a multi-variable polynomial equation with integer coefficients has an integer solution. Notably, there are many extensions of this problem, yet even over the rational numbers the decidability status is unknown. Poonen's lecture series will survey many problems related to undecidability and the technologies used in their proofs. It will touch on problems coming from topology, analysis, commutative algebra, dynamical systems, and probability, but culminating in recent work on extensions of Hilbert's tenth problem. The scope of these lectures will be fleshed out by talks from a collection of experts and early-career mathematicians. Up-to-date information about the conference can be found at: https://math.uark.edu/research/spring-lecture-series/<https://math.uark.edu/research/spring-lecture-series/> This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.