Research

Generally speaking, I am interested in low-dimensional topology, knot theory, embedding spaces and higher dimensional knot theory. At the moment my research focuses on various notions of equivalence of symmetric embeddings, such as equivariant isotopy, concordance, invertible concordance, etc. My current work focuses on these properties for knots in the 3-sphere and surfaces in the 4-sphere. 

1. Equivariant Double-Slice genus, Stabilization, and Equivariant Stabilization (2024)

To Appear in Algebraic & Geometric Topology -- (Slides)

2. Discretization of the Koch Snowflake Domain with Boundary and Interior Energies, with Carlos Lima, Gamal Mograby, Luke Rogers, and Alexander Teplyaev.  (2021)                              Fractals in Engineering: Theoretical Aspects and Numerical Approximations