Holonomic Techniques, Periods, and Decision Problems, Joël Ouaknine (Max Planck Institute for Software Systems, Germany) 


Abstract

Holonomic techniques have deep roots going back to Wallis, Euler, and Gauss. They have evolved in modern times as an essential subfield of computer algebra, thanks mainly to the work of Zeilberger and others over the past three decades. In this talk, Joël will give an overview of the area, and in particular, will present a select survey of known and original results on decision problems for holonomic sequences and functions. He will also discuss some surprising connections to the theory of periods and exponential periods, which are classical objects of study in algebraic geometry and number theory. He will particularly relate the decidability of specific decision problems for holonomic sequences to deep conjectures about periods and exponential periods, notably those due to Kontsevich and Zagier. 


Access

Joël will virtually visit our research unit Formal Methods in Systems Engineering. Join them here on Zoom. 

About 

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. They lie mainly at the intersection of dynamical systems and computation, using tools from number theory, Diophantine geometry, algebraic geometry, and mathematical logic.  


Joël studied mathematics at McGill University and received his 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 received the Arto Salomaa Prize (jointly with James Worrell), for outstanding contributions to Theoretical Computer Science, particularly to the theory of timed automata and the analysis of dynamical systems.

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