Gamma-positivity is an elementary property that polynomials with symmetric coefficients may have, which directly implies their unimodality. An important open problem on gamma-positivity is Gal Conjecture that the h-polynomial of every flag triangulation of a sphere is gamma-positive. In this talk, related to Gal conjecture, we discuss when a lattice polytope has a gamma-positive h*-polynomial.

In particular, we introduce several families of lattice polytopes which have gamma-positive h*-polynomials.

This talk is based on joint work with Hidefumi Ohsugi (Kwansei Gakuin University).