Symmetry, symmetry breaking, and phase transitions in interpolation inequalities

Mathphys Analysis Seminar

This lecture will be devoted to a review of recent results on nonlinear interpolation inequalities, branches of optimizers, and the classification of some phase transitions between symmetry and symmetry breaking regimes. When symmetry occurs, spectral and entropy methods can be used to obtain improved inequalities, improved rates of convergence for the corresponding nonlinear diffusion flows, and stability results.