Things we know, and things we do not, about knots

Document Type

Presentation Abstract

Presentation Date

11-3-2025

Abstract

In this talk, by knots I will mean circles embedded in three-dimensional space. I’ll start with background and some history, spend some time on knot invariants, then turn to the geometric perspective on knot complements that was introduced by Thurston around 1980. Along the way, I’ll mention some significant open questions in the subject. I’ll finish by discussing recent progress on a couple of geometric questions, on hidden symmetries of and totally geodesic surfaces in hyperbolic knot complements.

Additional Details

November 3, 2025 at 3:00 p.m. Math 103

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