Research Focus
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.
Publications
- 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.
MATH Courses - Spring 2025
- MATH 2930 : Differential Equations for Engineers
- MATH 4900 : Supervised Research
- MATH 4901 : Supervised Reading