Vortices and polynomials

A number of connections between point vortex dynamics and the properties of complex polynomials or rational functions with roots and/or poles at the vortex positions are reviewed. Classical polynomials, such as the Hermite and Laguerre polynomials, have roots that describe vortex equilibria. Completely stationary vortex configurations with vortices of the same strength but positive or negative orientation are given by zeros of the so-called Adler-Moser polynomials. The geometrical characterization of the location of the stagnation points in a flow produced by an assembly of point vortices is addressed. The 1864 theorem of Siebeck provides a beautiful solution to this problem.