Holonomic Techniques, Periods, and Decision Problems

Abstract: 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.

Parts of this talk will be based on the paper "On Positivity and Minimality for Second-Order Holonomic Sequences", arxiv.org/abs/2007.12282.

formal languages and automata theorylogic in computer sciencelogic

Audience: researchers in the discipline

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Online Worldwide Seminar on Logic and Semantics (OWLS)

Series comments: The Online Worldwide Seminar on Logic and Semantics is a new series of research talks, highlighting the most exciting recent work in the international computer science logic community. The scope of the seminar series is roughly that of the major computer science logic conferences such as LICS, ICALP and FSCD. It takes place on most Wednesdays, with a focus every other week on the work of young researchers.

In this time of restricted international travel, a key aim of this series is to provide a forum for the informal discussion and social interaction that is so important for the progress of science. To facilitate this, the seminar incorporates in virtual form a number of features more normally associated with physical meetings.

For more details, please visit the homepage. There is no need to register for the talks, just show up.

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