Explore the concept of comparing polytopes in combinatorial optimization through n-dimensional volume calculations in this 34-minute lecture by Jon Lee from the Hausdorff Center for Mathematics. Delve into the speaker's pioneering work with W. Morris from 1992 on fixed-charge problems, and discover new research conducted with E. Speakman on spatial branch-and-bound approaches to global optimization. Examine exact expressions for 4-dimensional volumes of parametric polytope families related to trilinear monomial convex relaxations. Gain practical insights for tuning spatial branch-and-bound implementations and improving modeling techniques in combinatorial optimization.