Explore an innovative approach to optimizing piecewise smooth shapes through a product shape manifold methodology in this 20-minute conference talk from GSI. Delve into the intricacies of shape optimization techniques and discover how this novel method can be applied to enhance the design and analysis of complex geometric structures. Gain insights into the mathematical foundations and practical applications of this cutting-edge approach, which has the potential to revolutionize fields such as engineering, computer graphics, and computational geometry.