Logic Seminar - Jonathan Kirby
| Dates: | 22 April 2026 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Jonathan Kirby (The University of East Anglia)
Title: Integration in finite terms and exponentially algebraic functions
Abstract: The problem of integration in finite terms is the problem of finding exact closed forms for antiderivatives of functions, within a given class of functions. Liouville introduced his elementary functions (built from polynomials, exponentials, logarithms and trigonometric functions) and gave a
solution to the problem for that class, nearly 200 years ago. The same problem was shown to be decidable and an algorithm given by Risch in 1969.
We introduce the class of exponentially-algebraic functions, generalising the elementary functions and much more robust than them, and give characterisations of them both in terms of o-minimal local definability and in terms of their types in a reduct of the theory of differentially closed fields.
We then prove the analogue of Liouville’s theorem for these exponentially-algebraic functions and give some new decidability results.
Joint work with Rémi Jaoui.
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