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Number Theory Seminar

Galois groups of random additive polynomials

Location:  Hill Center 425
Date & time: Tuesday, 18 October 2022 at 2:00PM - 3:00PM

Abstract: The Galois group of an additive polynomial over over a finite field is contained in a finite general linear group. We will discuss three different probability distributions on these polynomials, and estimate the probability that a random additive polynomial has a "large" Galois group. Our computations use a trick that gives us characteristic polynomials of elements of the Galois group, so we may use our knowledge of the maximal subgroups of GL(n,q). This is joint work with Lior Bary-Soroker and Alexei Entin.

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