Raymond van Bommel

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

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.