The article, “On foliations of the real projective plane defined by decomposable pencils of cubics,” developed out of Mr. Wall’s capstone project. While undergraduate research in mathematics is challenging, this project demonstrates that it is sometimes possible to obtain interesting new results even in the process of learning the larger mathematical theory. In this case, the analysis of certain families of planar dynamical systems posed some subtle questions of “real enumerative geometry.” Though problems of enumerative geometry have been studied for well over a century, the relevant techniques have been greatly advanced by recent developments in algebraic geometry and mathematical physics. As of 2022, Mr. Wall is a first-year doctoral student in mathematics at the University of North Carolina.

https://doi.org/10.1007/s00022-021-00623-1