MSGSS
The secret life of h-polynomials
A very common theme in combinatorics is to associate a polynomial to an object, and then show that the coefficients of this polynomial have “nice properties”. Desirable properties include: unimodality, log-concavity, gamma-positivity, real rootedness, etc. A common question asked when such a result is presented is: “why is this property relevant?”
In this talk we will go through some of these properties and how they appear in other areas of mathematics such as commutative algebra, algebraic geometry and differential geometry. Towards the end I will talk about recent results in joint work with Marge Bayer, Rick Danner, Marie Kramer and Yirong Yang on the real rootedness of the h-polynomial of triangulations of spheres arising from planar ternary graphs.