Iris Yoon, Swarthmore College
Event Date
2026-02-20
Event Time
04:00 pm ~ 05:00 pm
Event Location
Haverford College, room KINSC H012
PATCH Seminar (joint with Bryn Mawr, Haverford, Penn, and Swarthmore)
Abstract: Given a relation between sets A and X, one can build two simplicial complexes that each have A and X as the potential vertex set according to the relation. Dowker's Theorem states that the two simplicial complexes are homotopy equivalent. I will present short, new proofs of Dowker's Theorem using 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's Theorem to settings of relations among three (or more) sets.
In the morning background talk (at 11am, in room KINSC E309), I will provide a brief overview of how topology has been used in applied settings. The talk will provide some landscape of the field, but I will focus mostly on the topics relevant to my research.