Logic seminar: Alex Wilkie
| Dates: | 27 November 2024 |
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| Times: | 15:15 - 16:30 |
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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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ON ZILBER'S QUASIMINIMALITY CONJECTURE: AN ANALYTIC APPROACH
This conjecture concerns the expansion \mathbb{C}_{exp} of the complex exponential field by the usual complex exponential function and asserts that every definable subset of the complex numbers in this structure (even by a formula of the infinitary language allowing countable conjunctions and disjunctions) is either countable or co-countable, i.e. that \mathbb{C}_{exp} is quasiminimal. Now notions of minimality abound in model theory and often give rise to pregeometries, i.e. closure operators satisfying an exchange property which, in analytic situations, amounts to an inverse function theorem. I will clarify this remark in the context of Zilber's conjecture and then go on to discuss how it gives rise to a natural (Logic free) analytic continuation statement that implies a positive answer to Zilber's conjecture. I hope that there will be time left to mention some variants of this statement, in particular one concerning the solutions of ordinary differential equations of the form X' = P(X) where P is a polynomial map.
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Frank Adams 1
Alan Turing Building
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