Quantitative Stability and the Lojasiewicz inequality

Quantitative stability asks how a given functional grows near its minima or critical points. We will see how Lojasiewicz inequalities, which quantify the order to which a real analytic function on Euclidean space can vanish, can lead to quantitative stability results in regimes where explicit linearization around the minima is not possible. This talk covers joint work with O. Chodosh (Stanford), L. Spolaor (UCSD) and R. Neumayer (CMU).