Summer of Math Discovery: Two research projects on combinatorial polytopes (Andrés R. Vindas Meléndez, HMC)

This is a talk in two parts covering two projects that the speaker mentored over the summer of 2025. The first project deals with the study of polytopes that arise from the convex hulls of stack-sorting on particular permutations. The second project deals with the study of symmetric edge polytopes of a finite simple graph, a centrally symmetric lattice polytope whose vertices are defined by the edges of the graph. Both projects studied the (Euclidean, relative, or normalized) volumes of the respective combinatorially defined polytope.