Optimal Estimates for Neumann Eigenvalues

Explore cutting-edge research on optimal estimates for Neumann eigenvalues in this 50-minute conference talk by Antoine Henrot at BIMSA. Discover the groundbreaking result, awarded the 2024 Frontiers of Science Award in Mathematics, proving that the union of two identical balls maximizes the second non-trivial Neumann eigenvalue among sets of given volume. Learn about the topological argument used to achieve this finding. Delve into recent developments aimed at establishing optimal bounds for Neumann eigenvalues of convex sets in relation to their diameter or perimeter. Gain insights into collaborative work with Dorin Bucur, Beniamin Bogosel, Marco Michetti, Antoine Lemenant, and Ilaria Lucardesi in this advanced mathematical presentation.