Explore a mathematical lecture by Bruce Kleiner from the Hausdorff Center for Mathematics that delves into mean curvature flow in three-dimensional space and the resolution of the Multiplicity One Conjecture. Learn about evolving surfaces where the normal velocity component is determined by mean curvature, a concept first introduced in physics during the 1950s and extensively studied by mathematicians since the 1970s. The hour-long talk presents recent breakthroughs in understanding singularity formation and developing rigorous mathematical treatments of flow through singularities, leading to solutions for several longstanding conjectures. The presentation covers joint work with Richard Bamler that has advanced this important area of geometric analysis.