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College of Liberal Arts and Sciences | Mathematics

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October 22, 2019 | 3:00 p.m. - 4:00 p.m.
Category: Seminar
Location: Faculty/Administration #1140 | Map
656 W. Kirby
Detroit, MI 48202
Cost: Free

Speaker: Alison Miller

Title: Arithmetic statistics for knots and knot invariants

Abstract: Certain knot invariants related to the Alexander polynomial and the Seifert matrix can be viewed as arithmetic objects.  We investigate the question of how many different possible values can these invariants take for knots whose Alexander polynomial has bounded size?  We will see that this is really a number theory question, though it has applications to families of high-dimensional knots.  We present conjectured asymptotics and proven bounds for case of knots of genus 1, and will discuss what we expect for knots of higher genus.

For more information about this event, please contact Department of Mathematics at 313-577-2479 or