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Seminar

MT Research Seminar: Questions about isogenies, automorphisms, and bounds April 29, 2014 (01:30 PM PDT - 03:00 PM PDT)
Parent Program: Model Theory, Arithmetic Geometry and Number Theory
Location: MSRI: Simons Auditorium
Speaker(s) Barry Mazur (Harvard University)
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Abstract/Media

Let X be a modular curve - for example, the λ-line - and let α:X → X be an automorphism, say, that doesn't preserve the cusps. How does α affect the general Hecke orbit structure of X? In certain contexts - thanks to the work of a number of people in Model Theory - finiteness (of the intersection of one Hecke orbit with the image under α of another Hecke orbit) is known. I will describe a few of those known results, and formulate some questions about bounds connected to them.

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