Rafael D. Benguria Pontificia: Lieb-Oxford Bounds with Gradient Corrections

The Lieb-Oxford Bound on the indirect Coulomb energy, obtained by Elliott Lieb and Stephen Oxford in 1981, has played a major role in Atomic Physics. It has been used often in Mathematical Physics as a tool in proving different results in Stability of Matter problems. It has also been widely used in the Quantum Chemistry (DFT) community in order to estimate the Exchange and Correlation Energy. In this talk I will present a gradient correction to the Lieb-Oxford bound in two and three dimensions.