PoP Seminar Talk

The Skolem Landscape

Joël Ouaknine, Scientific Director
Monday, 20 May, 2024; 2:00pm
GHC 4303
Host: Frank Pfenning

Abstract

The Skolem Problem asks how to determine algorithmically whether a given linear recurrence sequence (such as the Fibonacci numbers) has a zero. It is a central question in dynamical systems and number theory, and has many connections to other branches of mathematics and computer science. Unfortunately, its decidability has been open for nearly a century! In this talk, I will present a survey of what is known on the Skolem Problem and related questions, including recent and ongoing developments.

Bio

Joël Ouaknine is a Scientific Director at the Max Planck Institute for Software Systems in Saarbrücken, Germany. His research interests straddle theoretical computer science and mathematics, and lie mainly at the intersection of dynamical systems and computation, making use of tools from number theory, Diophantine geometry, algebraic geometry, and mathematical logic. Joël studied mathematics at McGill University, and received a PhD in Computer Science from Oxford in 2001. He subsequently held postdoc positions at Tulane University and Carnegie Mellon University, and became Full Professor of Computer Science at Oxford in 2010. He received the Roger Needham Award in 2010, an ERC grant in 2015, and was elected member of Academia Europaea in 2020; the same year he also received the Arto Salomaa Prize (jointly with James Worrell), for “outstanding contributions to Theoretical Computer Science, in particular to the theory of timed automata and to the analysis of dynamical systems”. He was elected Fellow of the ACM in 2021 for “contributions to algorithmic analysis of dynamical systems”.