Monday, August 20: A student of Kevin Buzzard, in what would be a Master's thesis in the U.S., proved that for any integers $A,B,$ both the inhomogeneous polynomials $$x^2 + x y + 6 y^2 + z^3 + A z^2 + B z$$ and $$x^2 + x y + 8 y^2 + z^3 + A z^2 + B z$$ are universal, they integrally represent all integers. He also did a fixed one, $$2x^2 + x y + 2 y^2 + z^3 + z.$$ So the hard case really is these non-universal ones.