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Tuesday, November 28, 2023
2:30 PM - 3:45 PM

Algebra and Geometry Seminar

Conjugacy classes of derangements in finite groups of Lie type
Daniele Garzoni, Department of Mathematics, USC,

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.

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