**Abstract:** In 2012, Billey, Burdzy, and Sagan showed that given a positive integer $n$ and a subset $S \subset \{1,2, \ldots, n\}$ the number of permutations of length $n$ with peak set $S$ is $2^{n-|S|-1}p_S(n)$, where $p_S$ is a polynomial (now called the peak polynomial corresponding to $S$). In 2014, Billey, Fahrbach, and Talmage conjectured that the complex roots of peak polynomials of degree $m-1$ all lie within a circle of radius $m$, and they have real parts greater than $-3$. In this talk I will define descent polynomials, share a conjecture that states the roots of descent polynomials of degree $m-1$ satisfy the same bounds as those identified by Billey, Fahrbach, and Talmage, and discuss a number of partial results in support of these two conjectures. This is based on joint work with Alexander Diaz-Lopez, Pamela E. Harris. Mohamed Omar, and Bruce Sagan. In the process of explaining these conjectures, I will also share some experiences from my time working with undergraduate students on research at FGCU and organizing the Underrepresented Students in Topology and Algebra Research Symposium (USTARS).