A review about Lieb-Thirring inequalities

Michael Loss
Georgia Institute of Technology

Lieb-Thirring inequalities are estimates of certain means of eigenvalues for Schr\"odinger operators in terms of the potential. They were invented by Lieb and Thirring in 1975 to give a simple proof of Stability of Matter. Because of its close connections to the calculus of variations and semi-classical analysis, calculating good constants in these inequalities has become a lively research endeavor with beautiful contributions notably by Lieb and Laptev -- Weidl. In this talk some of the ideas will be presented that led to recent progress in this field.