Seminar
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| Location: | SLMath: Online/Virtual |
This seminar will focus on Diophantine problems in a broad sense, with a view towards (but not limited to) interactions between Number Theory and Logic. Particular attention will be given to topics with the potential of further developments in the context of this MSRI scientific program. This will provide an opportunity for researchers to update on new results, techniques and some of the main problems of the field.
To participate in this seminar, please register here: https://www.msri.org/seminars/25206
Torsion Values Of Sections, Elliptical Billiards And Diophantine Problems In Dynamics
To participate in this seminar, please register here: https://www.msri.org/seminars/25206
Abstract:
We shall consider sections of (products of) elliptic schemes, and their "torsion values". For instance, what can be said
of the complex numbers b for which (2, \sqrt{2(2-b)}) is torsion on y^2=x(x-1)(x-b)?
In particular, we shall recall results of "Manin-Mumford type" and illustrate some applications to elliptical billiards. Finally, we shall frame these issues as special cases of a general question in arithmetic dynamics, which can be treated with different methods, depending on the context.
(Most results refer to work with Pietro Corvaja and David Masser.)
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| H.264 Video | 25179_28677_8672_Torsion_Values_of_Sections__Elliptical_Billiards_and_Diophantine_Problems_in_Dynamics.mp4 |