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Speaker:

Alina Ostafe
Affiliation:

University of New South Wales/MPIM
Date:

Wed, 04/09/2024 - 14:30 - 15:30
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar In this talk we address an open question in arithmetic dynamics regarding the frequency of primes modulo which all the iterates of a polynomial remain irreducible. More precisely, for a class of integer polynomials $f$, which in particular includes all quadratic polynomials, we show that, under some natural conditions, the set of primes $p$ such that all iterates of $f$ are irreducible modulo $p$ is of relative density zero. Our results rely on a combination of analytic (Selberg's sieve) and Diophantine (finiteness of solutions to certain hyperelliptic equations) tools, which we will briefly describe. Joint wok with Laszlo M\’ e rai and Igor Shparlinski (2021, 2024).

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