Schr\"odinger Operators with Many Bound States
  Consider the Schr\"odinger operators $H_{\pm}=-d^2/dx^2\pm V(x)$. We present a method for estimating the potential in terms of the negative eigenvalues of these operators. Among the applications are inverse Lieb-Thirring inequalities and several sharp results concerning the spectral properties of $H_{\pm}$. 
David Damanik (Caltech), Christian Remling (Univ. Osnabr\"uck)