Abstract: In this talk I will present a new lower bound on the indirect Coulomb energy in two dimensional quantum mechanics in terms of the single particle density of the system. The new universal lower bound is an alternative to the Lieb--Solovej--Yngvason bound with a smaller constant, $C=(4/3)^{3/2}\sqrt{5 \pi -1} \approx 5.90 < C_{LSY}= 192\sqrt{2 \pi} \approx 481.27$, which also involves an additive gradient energy term of the single particle density. I will also review the analogous situation in 3-d. In 2-d this is joint work with P. Gallegos and M. Tusek. In 3-d is a joint collaboration with G. Bley and M. Loss.