Logic seminar: David Meretzky
| Dates: | 7 May 2025 |
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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, Adults, Alumni, Current University students |
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Title: Differential Galois theory with new algebraic constants.
Abstract: A well-known counterexample due to Seidenberg shows that Picard-Vessiot extensions need not exist for arbitrary ordinary homogeneous linear differential equations over arbitrary differential fields. A positive result from Kolchin's school at around the same time (1955-56) shows that inside of a differential closure one can always find a fundamental system of solutions to such an equation over the base field which introduces a Galois extension's worth of new constants. I will give a model theoretic account of the structure of differential field extensions generated by fundamental systems of solutions which introduce a finite (algebraic) extension's worth of new constants, detailing the relationship to the Galois groupoid arising from internality data, and describing a partial Galois correspondence. I will discuss points of contact with Umemura's quasi-automorphic extensions introduced in 1996.
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Frank Adams 1
Alan Turing Building
Manchester
