Explore an advanced mathematical concept in this 19-minute conference talk from GSI, focusing on the approximate projection onto the tangent cone to the variety of third order tensors of bounded rank. Delve into the intricacies of tensor algebra, geometric optimization, and algebraic geometry as the speaker presents their research findings and methodologies. Gain insights into the challenges and potential applications of this complex mathematical problem, suitable for graduate-level mathematicians and researchers in related fields.