Symmetric Edge Polytopes - Clustering, Degree Sequences, and Graphs with Few Edges

Explore a 52-minute lecture from the University of Kentucky's Benjamin Braun at IPAM's Computational Interactions between Algebra, Combinatorics, and Discrete Geometry Workshop, delving into the fascinating world of symmetric edge polytopes and their relationship to finite simple connected graphs. Discover recent collaborative research with Kaitlin Bruegge and Matthew Kahle examining the number of facets in symmetric edge polytopes, a reflexive lattice polytope structure that has garnered significant attention from geometric and algebraic combinatorics researchers. Learn about graph clustering metrics, degree sequences, and findings from empirical sampling across various random graph models, while gaining insights into both the geometric structure and algebraic-combinatorial invariants of these mathematical objects.