Research Area: Low-dimensional topology
I am particularly interested in algebraic invariants of knots in 3-manifolds and loops in surfaces. My recent projects have focused on problems in flat virtual knot theory, working with knots and links that are combinatorial models of curves on surfaces.
I am also interested in developing course materials that allow students to actively engage with their mathematical learning, using their curiosity, props, and activities to build mathematical ideas.
Complexity of virtual multistrings, Comm. Contemp. Math. (2021), https://doi.org/10.1142/S0219199721500668.
Multistring based matrices, J. Knot Theory Ramifications 29(6) (2020), 2050038.
Minimizing intersection points of curves under virtual homotopy, with V. Chernov and R. Sadykov, J. Knot Theory Ramificiations 29(3) (2020), 2050007.