Dowker duality - applications, short new proofs, and generalizations

I will discuss recent applications of Dowker complexes in cancer biology and neuroscience. I will then present short, new proofs of Dowker duality using various poset fiber lemmas. I will introduce modifications of joins and products of simplicial complexes called relational join and relational product complexes. Using the relational product complex, I will then discuss generalizations of Dowker duality to settings of relations among three (or more) sets.