For a polynomial f∈ℚ[x], Hilbert’s irreducibility theorem asserts that the fibre f-1(a) is irreducible over ℚ for all values a∈ℚ outside a “thin” set of exceptions Rf. The problem of describing Rf is closely related to determining the monodromy group of f, and has consequences to arithmetic dynamics, the Davenport-Lewis-Schinzel problem, and to the polynomial version of the question: “can you hear the shape of the drum?”. We shall discuss recent progress on describing Rf and its consequences to the above topics.
Based on joint work with Joachim König.
This talk relates to this arXiv paper.
This video is part of the Institute for Advanced Study‘s Number theory seminar.
