Explore the concept of extension complexity in polytopes through this 46-minute lecture by Lisa Sauermann at the Hausdorff Center for Mathematics. Delve into the representation of complex polytopes as projections of simpler ones, and understand how extension complexity quantifies this phenomenon. Learn about its significance in combinatorial optimization. Examine recent findings on the extension complexity of random d-dimensional polytopes in fixed dimensions, focusing on convex hulls of random points on the unit sphere or within the unit ball. Gain insights from joint research conducted with Matthew Kwan and Yufei Zhao, advancing your understanding of geometric complexity and its applications.