Reducible fibers and monodromy of polynomial maps
Reducible fibers and monodromy of polynomial maps
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Danny Neftin, IAS
In-Person and Online Talk听
Zoom link:听听
Passcode: The three digit integer that is the cube of the sum of its digits
For a polynomial $f\in \mathbb Q[x]$, Hilbert's irreducibility theorem asserts that the fiber $f^{-1}(a)$ is irreducible over $\mathbb Q$听for all values $a\in \mathbb Q$听outside a "thin" set of exceptions $R_f$. The problem of describing $R_f$听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 $R_f$听and its consequences to the above topics.
Based on joint work with Joachim K枚nig.