Overview
I am interested in mathematical physics, topology, and algebra. More specifically, I study quantum invariants of knots and 3-manifolds, and in particular connections to hyperbolic geometry; much of my work is inspired by or related to the Volume Conjecture. Physically this has to do with Chern-Simons theories with complex (noncompact) gauge group.
Current Appointments & Affiliations
Phillip Griffiths Assistant Research Professor
·
2023 - Present
Mathematics,
Trinity College of Arts & Sciences
Assistant Research Professor of Mathematics
·
2021 - Present
Mathematics,
Trinity College of Arts & Sciences
Recent Publications
Octahedral coordinates from the Wirtinger presentation
Journal Article Geometriae Dedicata · August 1, 2025 Let ρ be a representation of a knot group (or more generally, the fundamental group of a tangle complement) into SL2(C) expressed in terms of the Wirtinger generators of a diagram D. This diagram also determines an ideal triangulation of the complement cal ... Full text CiteOctahedral coordinates from the Wirtinger presentation
Preprint · April 29, 2024 Link to item CiteSurgery calculus for classical $\operatorname{SL}_2(\mathbb{C})$ Chern-Simons theory
Preprint · October 17, 2022 Link to item CiteEducation, Training & Certifications
University of California, Berkeley ·
2021
Ph.D.