17T7 as a Galois group over Q through Hilbert modular forms

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• Raymond van Bommel (Bristol)
• Tuesday 11 February 2025, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Rong Zhou.

The inverse Galois problem asks whether every finite group can be realised as the Galois group of a finite Galois extension of Q. For a long time, the so-called group 17T7, acting transitively on a set of 17 elements, was the smallest group in the transitive group ordering for which no such extension of Q was known. In this talk, I will describe joint work with Edgar Costa, Noam Elkies, Timo Keller, Sam Schiavone, and John Voight, in which we use certain Hilbert modular forms to find such an extension.

This talk is part of the Number Theory Seminar series.

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