3 papers
math.AG2022
Circles of Apollonius two ways
Stephen McKean
Because the problem of Apollonius is generally considered over the reals, it suffers from variance of number: there are at most eight circles simultaneously tangent to a given trio…
math.AG2020
An arithmetic enrichment of Bézout's Theorem
Stephen McKean
The classical version of Bézout's Theorem gives an integer-valued count of the intersection points of hypersurfaces in projective space over an algebraically closed field. Using wo…
math.AT2019
The trace of the local -degree
Thomas Brazelton, Robert Burklund, Stephen McKean +2
We prove that the local -degree of a polynomial function at an isolated zero with finite separable residue field is given by the trace of the local -deg…