Andrew Scoones (University of York) - On the abc Conjecture in Algebraic Number Fields
| Dates: | 29 March 2022 |
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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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| Speaker: | Caleb Springer |
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Abstract : While the abc conjecture remains open, much work has been done on weaker versions, and ongeneralising the conjecture to number fields. Stewart and Yu were able to give an exponential bound formax{a, b, c} in terms of the radical over the integers, while Györy was able to give an exponential boundfor the projective height H(a, b, c) in terms of the radical for algebraic integers. We generalise Stewart and Yu’s method to give an improvement on Györy’s bound for algebraic integers, before discussing applications to the effective Skolem-Mahler-Lech problem and the XYZ conjecture.
Speaker
Caleb Springer
Organisation: University College London
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Frank Adams 1
Alan Turing Building
Manchester
