Holonomic techniques, periods, and decision problems
Joël Ouaknine gave an invited talk on holonomic techniques, periods, and decision problems at Foundations of Software Technology and Theoretical Computer Science conference (FSTTCS 2020). During his talk Joël presented some of our ongoing work on inequality decision problems for low-order holonomic sequences (see here). The abstract and recording for the talk are given below.
Holonomic techniques have deep roots going back to Wallis, Euler, and Gauss, and have evolved in modern times as an important subfield of computer algebra, thanks in large part to the work of Zeilberger and others over the past three decades. In this talk, I 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. I 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; in particular, I will relate the decidability of certain decision problems for holonomic sequences to deep conjectures about periods and exponential periods, notably those due to Kontsevich and Zagier.