With Ulrich Daepp, Gorkin is the author of the undergraduate textbook
Reading, Writing, and Proving: A Closer Look at Mathematics (Springer, 2003; 2nd ed., 2011). With Daepp, Andrew Shaffer, and Karl Voss, she is the author of
Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other (
Carus Mathematical Monographs, MAA Press, 2018). The book studies a connection between
Blaschke products,
Poncelet's closure theorem, and the
numerical range of
matrices. A Blaschke product is a certain kind of mapping of the
unit disk in the
complex plane to itself, and the ones considered in the first part of the book have order three (they map the
unit circle three-to-one to itself, so that each point on the unit circle has three preimages). These triples of preimages form triangles that are all inscribed in the unit circle, and (it turns out) they all circumscribe an ellipse. Thus, they form an infinite system of polygons inscribed in and circumscribing two conics, as Poncelet's theorem describes. The ellipse is the boundary of the numerical range of a certain matrix derived from the Blaschke product, a region within which the
eigenvalues of the matrix can be found, and in this case the eigenvalues are at the
foci of the ellipse. The book tells "a story of discovery" outlining these connections, extends similar results to Blaschke products of higher order, and outlines a plan for further research in this area. ==Recognition==