Explore a mathematical lecture on context-free orderings on free products presented by Zoran Sunic from Hofstra University. Delve into the concept of context-free ordering on finitely generated groups, where the positive cone can be represented by a context-free language recognized by a push-down automaton. Discover three constructions of Cantor sets of orderings on free groups of finite rank, each featuring a dense subset of context-free orders. Examine how these orderings extend to lexicographic ordering on positive submonoids, short-lex ordering, and discrete orderings. Learn about the application of these results to free products with regularly ordered free factors, including explicit constructions of orderings on A*B where A is a convex subgroup. This 58-minute talk, part of the Workshop on Orderable Groups, provides valuable insights into advanced mathematical concepts in group theory and order theory.