I will give a brief review of prior works on flat knot theory and then talk about some results we have in the attempt to push the boundary of flat knot tabulation.
I will present some examples comparing based matrices and (algebraic) sliceness of flat knots to the Seifert matrices and (algebraic) sliceness of classic knots, and introduce a matrix-based method to calculate the Jones-Krushkal polynomial. I will present some conjectures about flat knot concordance.