Explore a comprehensive lecture on solving Sobolev-supercritical elliptic problems, focusing on overcoming the lack of compactness due to absent Sobolev embeddings. Delve into how symmetry and monotonicity properties can be leveraged to address this challenge. Examine a recent breakthrough in finding new axially symmetric solutions to a semilinear elliptic equation, achieved through a combination of variational and topological techniques. Learn about this collaborative work involving A. Boscaggin, F. Colasuonno, and T. Weth, presented by Benedetta Noris at the Hausdorff Center for Mathematics.