David Freund

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.