The Tangle Hypothesis

Document Type

Presentation Abstract

Presentation Date

4-20-2026

Abstract

Inspired by anyon dynamics (eg, the dynamics of electrons confined to 2 dimensional material), one can achieve a knot invariant from pure category theory. The Jones polynomial, and Alexander polynomial, are examples of such knot invariants.

In this talk, I’ll physically motivate this construction, followed by a mathematically motivated tour of the construction. Along the way, I’ll allude to the challenging aspects of the construction, and indicate the techniques used to resolve such. All the while, I'll draw pictures of knots.

Additional Details

April 20, 2026 at 3:00 p.m. Math 103

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