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I am interested in low-dimensional topology and 3-manifold geometry, and especially quantum topology. Below are a list of publications and talks given. I will flesh this section out more as I develop as a researcher.
Research Talks
Research Talks
Synthetic Geometry in Hyperbolic Simplices
Synthetic Geometry in Hyperbolic Simplices
MAA Mathfest 2021
Outstanding Student Paper Section Presentation Award
JMM 2022
BUGCAT 2021
EPaDel Spring 2021
IUP Scholar's Forum 2021
On the Closure of the Symmetric Difference Property
On the Closure of the Symmetric Difference Property
EPaDel Fall Section Meeting 2021
Bloomsburg University MADS Seminar; Fall 2021
Expository Talks
Expository Talks
Temple University Graduate Seminar
Temple University Graduate Seminar
How to Build a 3-manifold (Fall '24)
Braid Groups and Cryptography (Fall' 23)
Temple University JR. Geometry Seminar
Temple University JR. Geometry Seminar
Skein Modules of 3-manifolds (Spring '25)
Quantum Representations of Mod(S) (Fall '24)
Operator Invariants of Tangles (Spring '24)
The Jones Polynomial and Knot Surfaces (Spring '24)
Skein Invariants of 3-manifolds (Fall '23)
Bloomsburg University MADS Seminar
Bloomsburg University MADS Seminar
Knots and why we care (Fall 2024)
Publications & Preprints
Publications & Preprints
Synthetic Geometry in Hyperbolic Simplices with Barry Minemyer. Involve, a Journal of Mathematics. 15 (2023), Issue 5, 885-904. arXiv.
ABSTRACT: Let τ be an n-simplex and let g be a metric on τ with constant curvature κ. The lengths that g assigns to the edges of τ, along with the value of κ, uniquely determine all of the geometry of (τ,g). We focus on hyperbolic simplices (κ=−1) and develop geometric formulas which rely only on the edge lengths of τ. Our main results are distance and projection formulas in hyperbolic simplices, as well as a projection formula in Euclidean simplices. We also provide analogous formulas in simplices with arbitrary constant curvature κ.
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