Chris McDaniel: 3 takes on Almkvist's Conjecture

In the 1980s, Gert Almkvist conjectured that a certain two parameter family of univariate polynomials has unimodal coefficients in almost all cases. I will discuss three different perspectives on this problem, including Almkvist's original attempt using complex analysis, as well as some recent results and conjectures using combinatorics and commutative algebra.