Analytically One Dimensional Planes and CLP

This lecture presents joint research by Sylvester Eriksson-Bique and Guy C. David exploring the connection between conformal dimension and analytically one dimensional planes. Discover how the researchers established a surprising implication between two seemingly unrelated problems: whether a two-dimensional version of the Laakso diamond space attains its conformal dimension, and whether there exists a metric and measure on the two-dimensional sphere satisfying the Poincaré inequality with a one-dimensional Cheeger co-tangent bundle. Learn about their finding that a positive answer to the first problem implies a positive answer to the second, despite the first seeming possible and the second seemingly impossible. The presentation also covers interesting connections to three-dimensional hyperbolic buildings, providing insights into this complex area of mathematical research.