Algebra isomorphism, random matrices, and character sums

Abstract: In this talk, we show how the algorithmic problem of algebra isomorphism naturally leads to questions about random matrices over finite fields. To settle these questions, we need to extend both the generating function approach as in Neumann and Praeger (J. London Math. Soc., 1998) and the characteristic sum method of Gorodetsky and Rodgers (Trans. Amer. Math. Soc., 2021). Several open questions remain for further exploration.

Joint work with Tiange Li, Yinan Li, Dacheng Tao, Yingjie Wang. Paper available at https://arxiv.org/pdf/2604.00591.

number theory

Audience: researchers in the topic

UNSW Number Theory Seminar

Series comments: The UNSW Number Theory Seminar has been running in the School of Mathematics and Statistics, UNSW Sydney, since 2015. The seminar usually takes place every two weeks on Wednesdays, 2 - 4 pm, with two talks scheduled each seminar, followed by refreshments and discussions.