Explore a 50-minute lecture on geometric objects associated with planar bipartite graphs presented by Pavel Galashin from the University of California, Los Angeles. Delve into the process of associating various topological and geometric data to planar bipartite graphs within a disk. Discover examples of objects such as knots, cluster varieties, higher secondary polytopes, and critical varieties. Examine the relationships between these objects and gain insights from joint research with T. Lam, A. Postnikov, and L. Williams. Recorded on March 26, 2024, as part of IPAM's Statistical Mechanics and Discrete Geometry Workshop at UCLA, this talk offers a deep dive into the intersection of graph theory and geometry.