Explore the groundbreaking research on finite point blowup for the critical generalized Korteweg-de Vries equation in this 40-minute conference talk by Didier Pilod at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the significant advances made in studying blow-up phenomena for the critical gKdV equation over the past two decades. Discover the recent breakthrough in constructing solutions that blow up in finite time, concentrating the ground state at a finite point with an unprecedented blow-up rate. Learn about the implications of this discovery for understanding possible blow-up rates in the equation. Gain insights from the joint work of Didier Pilod and Yvan Martel, presented as part of the Thematic Programme on "Nonlinear Waves and Relativity" at ESI.