Tuesday, November 28, 2023

2:30 PM -
3:45 PM

# Algebra and Geometry Seminar

Conjugacy classes of derangements in finite groups of Lie type

*USC Kaprelian Hall Rm 414*

Given a group G acting on a set, an element of G is called a derangement if it acts without fixed points. Luczak-Pyber and Fulman-Guralnick showed that if G is a finite simple group acting transitively, then the proportion of derangements is bounded away from zero absolutely. I will discuss a conjugacy-class version of this result for groups of Lie type, obtained in joint work with Sean Eberhard. I would like to discuss mainly two things: (i) why derangements are interesting, and (ii) explain some interesting connections between the proof of the result and the subject of "anatomy of polynomials", which essentially studies divisors of random polynomials.

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For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].