Manchester Number Theory Seminar - Martin Orr
| Dates: | 25 March 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, Current University students |
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Speaker: Martin Orr (University of Manchester)
Title: Effectivity and very unlikely intersections in abelian varieties using G-functions
Abstract: A special case of the Zilber-Pink conjecture, proved by Habegger and Pila, states that a generic curve C in an abelian variety A has only finitely many "unlikely intersections", that is, intersections of C with subgroups of A of codimension at least 2. One important ingredient in the proof is a bound for the height of these intersection points. G-functions give a new method of proving such a height bound for intersections with subgroups of large codimension ("very unlikely intersections"). A benefit of the G-functions method is that it is in principle effective. In this talk I will discuss some of the challenges hiding in the words "in principle" when applying the G-functions method to obtain effective height bounds.
Room: Frank Adams 1
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Frank Adams 1
Alan Turing Building
Manchester
